Andre Sokol, a 59-year-old unemployed carpenter, is an example of someone who won’t be helped by the law and will continue to rely on the Arlington clinic, which, at an given time, provides care to about 1,600 people. He lost his health-care benefits when he left his job in the construction industry several years ago to care for his longtime girlfriend, who was diagnosed with ALS, and his mother, who was battling dementia. Two years ago, the women died within two months of each other. Sokol had no job, no income and no place to live.

In January, Sokol had quadruple bypass surgery at Virginia Hospital Center, which absorbed the costs. He didn’t qualify for Medicaid because Virginia doesn’t allow single men, no matter how poor, on Medicaid, unless they’re disabled. The state has one of the strictest eligibility standards in the country. That would change if the state expanded its program under the health law.

At the same time, Sokol’s income is too low to allow him to get federal subsidies to help pay for a private policy on the exchange. (The law assumed people with incomes below 100 percent of the poverty level, or about $11,500, would be covered by Medicaid, but many states balked at enlarging their programs after the Supreme Court said the expansions were optional.) Arlington Free Clinic officials said about half of their patients are in the same situation: They are below the poverty line but aren’t eligible either for Medicaid or subsidies to buy insurance.