Like ride-share drivers, aides often work for multiple agencies, following different safety protocols. Clients, too, might have a night aide from one agency, a morning aide from another, weekend aides from a third and family members filling the gaps.

So risks pass between aides and clients, but also among aides and other aides, family members and fellow subway riders. For the homebound, any health setback might mean a trip to the emergency room, which for the aide means a marathon wait in the place where the virus is most clustered.

At RiseBoro Community Partnership, which sends 1,100 home care workers into 700 homes in Brooklyn and Queens, Glenmore Matthews, the vice president of home care, said he was trying to stagger travel times and to change routes to reduce risk on the subways.

He talked about the financial toll on agencies like his. Any missed visits means lost revenue. “If we don’t provide services, we cannot bill Medicaid,” he said. “It’s a domino effect.”

James Reynolds, a physical therapist who works for the New Jewish Home, said he tried to maintain social distancing when visiting clients, but it was not always possible. Many of his patients were recovering from falls, learning to regain balance. “So I have to stand close enough to assist,” he said.

Mr. Reynolds grasped a cruel irony: his care might be the thing that kills a patient. “I am looking at the risk and reward,” he said. “If a patient is a fall risk but has family around them, I might not seek more visits, because those visits put them at risk.”