The recession has prompted some state and local governments to pare programs that benefit illegal immigrants. And although illegal immigrants may account for about seven million of the country’s 46 million uninsured, the health care bills being negotiated by Congress exclude them from expansions of subsidized public insurance. (The House bill that passed on Nov. 7 would allow illegal immigrants to buy policies at full cost on government-run exchanges, while legislation being considered in the Senate would forbid it.)

Calling it “a horrible situation,” Mr. Correll said that governments at all levels had decided that immigrants were not their problem. “But somehow,” he said, “they’ve become Grady’s problem, which seems totally unfair.”

Some of the Grady dialysis patients have chosen to return to their countries, encouraged by the hospital’s offer of free airfare, cash payments, three months of paid dialysis and assistance in seeking insurance or other long-term remedies. Others are trying their luck in states where Medicaid policies may be less restrictive.

But most remain in Atlanta, taking full advantage of a last-minute offer by the hospital, in response to a lawsuit, to pay for three months of dialysis at commercial clinics. They are hopeful that the reprieve will buy time for the lawsuit to progress or for private dialysis providers to take them as charity cases.

What they fear, however, is that their already fragile lives will soon be reduced to a frenzied search for their next dialysis, most likely in an emergency room after a descent into crisis.

Looking for a Better Life

They need only look to Ms. Perez to see what the future may hold.

After hearing that the clinic would close, Ms. Perez, 32, set out for Alabama on Sept. 6 because cousins told her they might be able to procure dialysis there. Grady was not yet offering its deal for three months of treatment, and instead gave her $1,300, enough to cover dialysis for a week or two.

Ms. Perez said the money was quickly spent on rent, food and transportation. After going without dialysis for 16 days, she walked into an emergency room near Birmingham, which found that the potassium levels in her blood were high enough to require immediate filtration. Eight days later, she did the same at another Birmingham hospital.