It’s physically demanding work that pays poorly — the median wage for home care workers was $10.49 an hour in 2016, P.H.I. reports — and usually doesn’t include benefits. The aides, mostly women, who serve in this crucial but low-income role frequently qualify for federal programs like food stamps or Medicaid.

Their advocates have long argued for ways to improve these jobs, with more training and higher pay. For now, though, what P.H.I. calls the “caregiving gap” has been filled by immigrants.

The number of immigrants in direct care ballooned from 520,000 in 2005 to approximately one million in 2015, including those who work independently through state home care programs, P.H.I. estimates. In New York, California, New Jersey and Florida, more than 40 percent of direct-care workers are immigrants.

If large numbers of immigrants become unable to work or fearful of attracting unwanted attention, “this is going to create tremendous strain,” Dr. Stone said. Already, “we’ve heard of nursing homes that have shut down, or stopped admissions, because they could not hire enough people.”

Excluding the gray market, the majority of aides and nursing assistants are American citizens. But P.H.I. has calculated that nearly 35,000 come from Haiti, El Salvador, Nicaragua and Honduras, whose immigrants have had temporary protected status in the United States.

The administration has so far terminated T.P.S. status for Haitians, Salvadorans and Nicaraguans; other nationalities may follow. Immigrants from Sudan, whose T.P.S. status was also terminated, will have to leave the United States as early as this fall.