Pennsylvania’s governor was urgently preparing for a surge in Covid-19 cases last month when a private-equity-owned hospital said it would shut its doors unless the state secured a $40 million bailout.

Steward Health Care System LLC said it needed the money from the state in three days or “Easton Hospital will no longer be able to serve the community’s health-care needs and will be forced to close,” read a letter to the governor from Steward, which is owned by $43 billion New York investment firm Cerberus Capital Management LP.

Gearing up for an expected surge in patients, Pennsylvania didn’t want to lose any hospital beds, local and state officials said. “That’s how they kept the state hostage,” said Sal Panto, Easton’s mayor and a member of the hospital’s board of trustees.

Private-equity investors including Cerberus poured around $200 billion into U.S. health-care buyouts in the last decade. An aging population, strong health-care returns and huge cash piles for private-equity funds supported the deal making.

But a playbook that often includes loading portfolio companies with debt, selling assets to lock in profits and sometimes shutting hospitals is adding to the health-care system’s strains. Now the firms with struggling health-care investments find themselves in unwelcome fights with local communities.