“It destabilizes that work force,” said Robert Espinoza, vice president for policy at PHI, a group that advocates on behalf of personal care workers. “If you are seeing family members, children, neighbors being deported, threatened, and so on, the ability to be present on the job is undermined.”

The health care field’s reliance on immigrant labor makes it particularly vulnerable. According to census data Mr. Osterman analyzed, more than one-quarter of home health aides in 2015 were immigrants. The proportion in certain states is far higher, reaching nearly one-half in California and nearly two-thirds in New York.

The undoing of DACA may also herald the undoing of other programs that provide a steady source of immigrant labor in the health care sector. For example, the government can grant people from certain countries that have endured hardship, like natural disasters or civil wars, what it calls temporary protected status.

The overwhelming majority of workers granted that status hail from El Salvador, Honduras and Haiti, and many have flocked to low-paying health care professions as well.

“We know from surveys that T.P.S. recipients are highly represented in the work force in certain areas,” said Tom Jawetz, a vice president of the Center for American Progress, a think tank that favors more liberal immigration policies. “In particular, many — especially Haitians — work in home health care.”

The Trump administration has suggested it may not extend the program for Haitians when its most recent extension expires in January, raising questions about whether it will end the program for Hondurans and Salvadorans as well.

As a basic matter of economics, removing tens of thousands of workers from occupations that already suffer from a serious labor shortage — the Labor Department predicts that the country will need more than 1.25 million home health aides by 2024, up from about 900,000 in 2014 — generally has one unambiguous effect: driving up costs.