While most of the provider aid has been distributed, the Biden administration is expected to begin doling out the remaining funds, estimated at $25 billion of the original $178 billion, said Kristen O’Brien, a vice president for McDermott+Consulting in Washington, D.C. Hospitals are asking for more time to spend the money.

How the aid was spent has not been fully documented. While the larger hospital networks aggressively sought the funds from the start, smaller organizations, children’s hospitals and those in rural areas or serving large numbers of low-income patients had more difficulty securing the aid because of the way the funding formula was structured.

In a later round of funding decisions, officials with the Department of Health and Human Services reviewed applications more closely, and in some cases, reduced or denied requests, Ms. O’Brien said.

Grants given after the initial rush were more targeted, to those hospitals in Covid hot spots or rural areas. A few large chains, including HCA Healthcare and the Mayo Clinic, returned at least some of the money, in the wake of disclosures that wealthier hospitals had received far more aid while reporting healthy profits.

Overall, the aid program did prevent hospital closings, said Ken Marlow, a lawyer with K&L Gates in Nashville, who advises hospitals. “We haven’t seen a real avalanche of these distressed hospitals coming on the market.”

But some may no longer be able to resist takeovers or mergers. “Those providers are potentially more distressed as a result of the stress of the pandemic and will have to be thinking hard about the future, their survival,” said Torrey McClary, a lawyer with Ropes & Gray who also counsels hospitals.