Altitude has had “more frequent communication” with the operator over the past month and has offered to provide assistance, said William Rothner, the firm’s president. He said Alliance had not requested any.

The lowest-rated homes were disproportionately operated for profit. Nearly half the residents of for-profit nursing homes lived in ones where the federal government found below-average staffing levels, compared with 23 percent of the residents of government or nonprofit facilities, according to a New York Times analysis of government data.

Genesis HealthCare, one of the country’s largest for-profit operators, exemplifies many of the pressures.

It rents the property for more than 70 percent of the 357 nursing homes it operates in the United States. Genesis’ shares trade for under $1, in part because of investor concern over its $1.6 billion in debt and the $5 billion outstanding on the value of its long-term leases. And nearly half the properties operated by Genesis scored two stars or lower in the government rankings.

Lori Mayer, a company spokeswoman, did not address Genesis’ financial situation and said any update would come when Genesis reports earnings next month. The company, she said, has taken a number of precautions to limit the spread of the highly contagious virus, which has torn through nursing homes from Washington State to New York.

The Times has tallied more than 4,000 nursing homes and other long-term care or elder facilities across the United States with coronavirus cases, based on reports by states and counties. More than 36,500 residents and staff members at those facilities have contracted the virus, and more than 7,000 have died. The names of most of those facilities have not been made public, but The Times has been able to identify at least 1,700 nursing homes on that list of facilities, which have reported 4,000 deaths.