“SpaceX bullied us from the beginning,” she said. “SpaceX employees did what they wanted.”

SpaceX, the maker of rockets and spacecraft controlled by Mr. Musk, among the world’s richest people, is facing off against a handful of households that have refused to sell their properties in this remote unincorporated village. Some 30 small ranch houses sit on a sandy spit of land near the Mexican border and Gulf of Mexico beaches, where SpaceX rockets roar into the sky and then return for a landing. Some come crashing back on land.

Villagers said Mr. Musk’s company has tried multiple times to buy them out. Some took the money, and SpaceX used the homes for its workers. Holdouts, at least seven of them, said they want more from a billionaire who’s after their dream vacation homes.

Mr. Musk and SpaceX didn’t respond to requests for comment. “We’ve got a lot of land with nobody around, so if it blows up, it’s cool,” Mr. Musk said of the South Texas location at a 2018 press conference, according to media reports.

It’s hard to know exactly why SpaceX wants residents’ houses, but indications are that it would be less of a security and safety issue not to have to worry about people living so close to launches. SpaceX has also indicated, based on the company’s job postings, that it would like to develop the area into a resort.

The Texas property scuffle is beginning to echo Old West tales of outsiders who pressure residents to give up land for development—including the classic threat of eminent domain.

In March, Mr. Musk tweeted “Creating the city of Starbase, Texas,” adding that this would happen through incorporation of the town—a tactic mining companies commonly used to create company towns. If incorporation were successful, Starbase officials would have the power of eminent domain.

If incorporated, depending on what type of municipality it became, the village could have a city manager, city counselor or mayor. There are about 14 people not connected to SpaceX living in Boca Chica Village now and a few more in surrounding areas that might be included. To incorporate the village, SpaceX would need to show that more than 200 people lived in the area and to garner a majority of their votes.

They could use that power to eject holdouts, said lawyers and law professors. They would also control the police, could issue tax-free municipal bonds and might attain statutory authority over the one road in and out of the village, opening and closing it at will, these legal experts said.

Eddie Treviño, Cameron County Judge—a position akin to the top county commissioner in most states—said he discussed the possibility of incorporation with SpaceX before Mr. Musk’s tweet, but “I didn’t think much of it at the time.” Boca Chica is in the county.

Eminent domain is “an option we may need to consider,” he said. The remaining Boca Chica Village residents might need to leave for their own safety, he said: “You don’t want individuals near rocket ships being tested and landing. We don’t want anyone to get hurt.”

Beach regulations

Since Mr. Musk founded his space company in 2002 in a converted Southern California warehouse, SpaceX has expanded to roughly 8,000 employees and has facilities from Florida to Texas to Washington state. It has focused on launching satellites for commercial uses, national security and weather forecasting.

At Boca Chica, SpaceX is developing a large new rocket, the Super Heavy, which aims to take people to the moon and Mars—a goal fortified in April when the National Aeronautics and Space Administration awarded SpaceX a contract to build a capsule to land astronauts on the moon.

Mr. Musk has had an assist from Texas. The state has allocated around $30 million in incentives for SpaceX’s Boca Chica operations. In 2013, state lawmakers passed a bill allowing Cameron County to temporarily close beach and beach-access points for spaceflight activity, despite the Texas constitution’s protection of the public’s free and unrestricted access to beaches.

The lawmakers behind the legislation didn’t respond to requests for comment. Texas House Rep. Alex Dominguez said that he has filed a bill to limit beach and beach-access closures at Boca Chica in response to constituent complaints but that he is working with SpaceX officials to try to improve beach access without limiting the company’s allowed closure hours, with measures like reducing the radius of the launch area and creating a fishing park in a separate area close to Brownsville. Mr. Dominguez said he hadn’t heard of any legal challenges regarding the 2013 legislation and didn’t believe it was a violation of the Texas constitution.

Cameron County officials have largely supported SpaceX operations, and most holdout residents said they thought the county was working to get them to leave.

Mr. Treviño said the county was “not working and would never work with SpaceX to harass any of the residents to leave the Boca Chica area.” He said the county wasn’t rolling over for SpaceX and had spoken with a developer about creating its own tourism business around the SpaceX activities. “We want SpaceX to succeed, but not at the expense of the community,” he said. “If they think they’ll be able to take over the highway or the beach, they’re mistaken.”

While some residents report that the county has told them they couldn’t get building permits they or their contractors requested to renovate houses in the village, public records show that SpaceX has been granted numerous building permits to fix up houses it owns, which it uses for its workers.

Dylbia Jeffries Vega, a Cameron County attorney, said the county did issue permits for two non-SpaceX affiliated houses: one for electrical work in 2021 and one for a renovation in 2019. The county rejected a permit application for Ms. Johnson’s rental house because there was no water source. Ms. Jeffries Vega said other residents didn’t file permit requests or only spoke to people about getting permits.

The county has granted SpaceX’s requests for beach-access closures, which include Highway 4, the only road that leads to Boca Chica. The county enforced closures even when they exceeded a 180-hour-a-year limit under SpaceX’s first agreement with the Federal Aviation Administration by a long shot, said David Newstead, a biologist with the Coastal Bend Bays & Estuaries Program, an environmental group, who has been tracking the closures.

According to a document released to The Wall Street Journal in response to a public-records request, the county is “reasonably anticipating litigation” against SpaceX regarding what the document said is the company’s violation of portions of its agreement with the county and the state, including issues related to road closures, building permits and security.

The county has learned that “SpaceX was not compliant with portions of an agreement between the County and SpaceX,” the document says. If SpaceX doesn’t rectify the lack of compliance, the document says, the county “may commence to terminate the agreement through the filing of a civil action against SpaceX.”

Mr. Treviño said there were continuing discussions to resolve a number of compliance issues that could result in litigation, but: “Just because lawyers are involved doesn’t always mean that litigation is imminent.”

An FAA spokesman said the agency approved in December 2020 a SpaceX request to increase closures to 300 hours annually. He said implementation and enforcement of those agreements was a local matter.

Mr. Treviño said that the county was complying with the expansion of hours granted by the FAA but that it wasn’t communicated to residents clearly. “I understand the frustration of the public,” he said, adding that the county was discussing with SpaceX how to make it easier for people to plan.

The village’s roots go back to 1967, when Chicago radio personality John Caputa developed the settlement on the Boca Chica peninsula, naming it Kennedy Shores after President John F. Kennedy, according to the Texas State Historical Association. He aimed his sales pitch of lots and homes at working-class Polish immigrants, selling houses for $12,500 apiece on the land, which hadn’t been developed previously due in part to its shallow soil and lack of freshwater.

A hurricane that year washed away Mr. Caputa’s plans and destroyed the sewage system and water-treatment plant. A few dozen homes had already been completed on two streets. In 1975, resident Stanley Piotrowicz incorporated the village and renamed it Kopernik Shores for astronomer Nicolaus Copernicus. The county judge abolished the incorporation two years later, and it came to be known as Boca Chica Village.

Living in the village meant bringing in water to store in tanks and dealing with balky septic systems. In 2001, the county agreed to a request by residents that it truck water to their tanks. The closest stores and restaurants open to the public were, and still are, 22 miles away in Brownsville.

It was a peaceful place with friendly neighbors and lots of birds, said Rosemarie Workman, 73, a retired finance manager. She and her husband, Jim Workman, 77, a retired truck driver, looked for years at retirement spots before buying their 1,154-square-foot brick house in Boca Chica Village in 2004. “The location was what we valued,” she said.

Land rush

SpaceX started buying land in Boca Chica in 2012 and broke ground on its launchpad in 2014, after the legislature passed the bill allowing for an exception to the constitution’s Public Beach Access act. In November 2013 testimony before the Texas House Appropriations Committee, Mr. Musk told legislators SpaceX would be “significant to the local economy and to the world.”

The activity was tolerable at first, residents said. But in 2019, SpaceX amped up operations, moving from a plan authorized by the FAA that allowed up to 12 launches a year of commercial-grade rockets to a more ambitious program involving the development, fabrication and testing of the Super Heavy. There was an influx of workers and trucks.

Residents said SpaceX, through a realty company, made a barrage of offers to buy their homes. In September 2019, Ms. Workman received a letter offering $155,700, which the letter said was three times the independently appraised fair market value, she said. The letter said the offer wasn’t negotiable.

The county’s official appraised value for Ms. Workman’s home was $34,473 when SpaceX made its offers. The county increased its appraisal to $141,573 for 2021, according to the county’s website. An appraiser Ms. Workman hired when SpaceX was making its offers valued it at $194,000, she said.

The Workmans received two more offers from SpaceX but neither surpassed $150,000, they said. Then another, $210,600, came with a phone call from SpaceX’s senior director of finance, David Finlay, who told them they had a week to respond or SpaceX would pursue a “different route,” said Ms. Workman. They declined the offer and are still living there.

Mary and Harvey Bloomer’s Boca Chica household received an email from Mr. Finlay on Sept. 29, 2020, confirming SpaceX’s $149,700 offer for the home. The email, which the Journal reviewed, warned them that their property would frequently fall into a hazard zone “in which no civilian would be permitted to remain.”

Mr. Finlay wrote that it was SpaceX’s final offer, adding: “Please be advised that should this offer expire, SpaceX may need to pursue alternative approaches” to making sure it could conduct launch operations within public-safety requirements. Mrs. Bloomer said the amount SpaceX offered was unacceptable. Mr. Finlay declined to comment.

Around the same time, SpaceX advertised for a resort manager to turn Boca Chica into “an epic place to live and work.” The manager would be responsible for planning activities such as kayaking and volleyball tournaments, according to the ad.

SpaceX so far has bought more than 112 parcels of land in the village, public records show. The company parks Airstream trailers in driveways and has built structures on land adjacent to the village.

Residents said Mr. Musk often stays at a house SpaceX bought in 2019, a modest 1,580-square-foot brick ranch house the county appraised in 2020 at $47,000 and in 2021 at $154,359.

Jim and Nancy Crawford, who live across the street, said they see him about once a week when they are there. The house has been renovated inside and sports a new roof and solar panels, according to the Crawfords, other residents and recent photos.

Rob Avery, 67, who has lived in Boca Chica Village since 2004, has photos of the 8-inch-deep tire tracks left by what he said were SpaceX trucks driving across his yard to a company-owned property. He said there were weeks of all-day-and-night construction on the homes SpaceX bought, with spotlights making it difficult to sleep.

Launch activity

When SpaceX launch activity picks up, Boca Chica residents find fliers left on their properties advising them to exit their homes during flight activities due to the possibility of damage from malfunctions.

In the past few months, multiple SpaceX rockets have exploded, breaking windows, scattering debris and causing brush fires, said residents and the Coastal Bend Bays & Estuaries Program that monitors SpaceX. On March 30, SpaceX’s fourth launch of its Starship prototype exploded, sending debris far and wide. Residents the Journal spoke with said none of them had been injured in the explosions.

Residents said that SpaceX offers to put them up at a hotel on South Padre Island during launches, about a 40-mile drive, but that they must pay for gas and food.

Residents complain about the closures of Highway 4. The Coastal Bend Bays & Estuaries Program and other environmental groups wrote to the FAA saying SpaceX was exceeding the limit “often with confusing and inadequate prior notifications and last-minute changes and revocations.”

Residents said county officials at checkpoints have stopped them for hours and that SpaceX security personnel have followed them in vehicles to their homes. Closures also mean a loss of public access to 8 miles of public beach, state-park land and a National Wildlife Refuge.

Mr. Treviño said the road closures were enforced to protect public health and safety.

“They act like they already own everything, including you and your house,” said Cheryl Stevens, who said she sold her Boca Chica house to SpaceX for more than the $139,500 they initially offered, moving out in October, after she deemed it unlivable due to the company’s activities.

Mr. Workman said a security guard, staying on the street while Mr. Musk was in town last fall, crossed his lawn and confronted him in his doorway about why he was using binoculars. He was watching birds, he said, and he told the guard so.

Now that SpaceX has shifted to more powerful rockets and more extensive operations, the FAA is conducting a full environmental review that goes beyond the hours of closure. Under SpaceX’s new plan, the allowed beach closures would almost triple.

“It’s a good economic development project for our area,” said Nick Serafy, chairman of the Cameron County Spaceport Development Corp., a nonprofit the state created to financially support space-related development. He said SpaceX originally promised at least 200 jobs but has created closer to 1,400, most filled by local residents. “We have not had an economic-development project like that,” he said, “one that produced seven times the jobs projected.”

Boca Chica Village residents have benefited from rising property values since SpaceX began buying houses there. A house that the county appraised at $34,473 in 2020, after a decade of staying around that level, is appraised at $141,573 in 2021.

‘Starbase, Texas’

County officials’ support has residents worried about Mr. Musk’s incorporation plans. In a March tweet, he posted a photo of himself with his son X Æ A-Xii and his son’s mother, the musician Grimes, under the heading “Starbase, Texas.”

Later that month, he tweeted: “Please consider moving to Starbase or greater Brownsville/South Padre area in Texas & encourage friends to do so!” In another tweet, he wrote: “Am donating $20M to Cameron County schools & $10M to City of Brownsville for downtown revitalization.” Mr. Musk’s foundation has since distributed $5 million to Cameron County schools but no money yet to Brownsville. Brownsville Mayor Trey Mendez said he is “working on a plan with them on how to use the funds.” He said the city and the Musk Foundation were in talks about where the money was most needed.

It isn’t clear whether SpaceX employees living temporarily in Airstream trailers would qualify as among the more-than-200 inhabitants Texas law requires for incorporation. The definition of an inhabitant is fairly loose under Texas law, said Alan Bojorquez, an Austin, Texas, lawyer and author of a book on Texas municipal law. Those workers could qualify, he said, “if there’s some documentation showing that’s where they live.”

Under Texas law, cities can’t use eminent-domain power for purely economic-development purposes. But the lawyers and law professors who specialize in land use and local-government law said the future Starbase could argue it needs to buy out remaining homeowners for public-safety reasons, which could be allowed.

Residents said they haven’t received any new offers from SpaceX this year. There is less noise and construction now, and SpaceX managers are now eager to help with issues like windows broken during launches, they said.

The purloined tank

Ms. Johnson spent her summers with her family at Boca Chica Beach while growing up in Brownsville. She saved enough as a social worker in Michigan to buy two modest houses in the village, using one as a rental to supplement maintenance of the other. Her plan was to retire in the village and then leave the homes to her two sons.

Her troubles started in the fall of 2019, she said, when someone stole her water tank. A few months later, she arrived at her rental house to find a window smashed with a brick. It appeared someone had been living at the house—a dresser and chair were pushed up against a door in one room, blocking entry. She filed a police report in January 2020.

The break-in coincided with the influx of SpaceX workers around that time, and Ms. Johnson notified a SpaceX manager about the break-in. She said that the manager agreed that the missing tank and break-in were probably the doing of company workers and that he said he would compensate for the damage and missing tank—he did, she said.

In June 2020, after Ms. Johnson found a renter for the house, she tried to get power turned on, she said, but the county told her she had to update her wiring, which she did. Then, she said, the county said it couldn’t turn on her power without a permit to upgrade the septic system. That turned out to be impossible without a supply of water, and Cameron County had cut off her water delivery after her tank disappeared.

The county declined to turn the water back on even though she had installed another tank, she said. The renter and income were lost. Ms. Jeffries Vega, the county attorney, confirmed the county rejected Ms. Johnson’s permit application because she didn’t have a water source.

The county’s Mr. Treviño said the county recently implemented a new policy to cut off water deliveries to any house that asked for a renewal of water service after a suspension for any reason. He said the county isn’t under a mandate to deliver water.

Now, Ms. Johnson is sitting tight, riding out rocket launches and crashes, hoping SpaceX will increase its offer for her homes. “Prior to SpaceX coming here,” she said, “there were no problems.”

—Alicia A. Caldwell contributed to this article.

Write to Nancy Keates at nancy.keates@wsj.com and Mark Maremont at mark.maremont@wsj.com

Corrections & Amplifications
Brownsville is 22 miles west of Boca Chica Village. An earlier version of this article incorrectly said Brownsville is 22 miles east. (Corrected on May 7.)