Ms. Laffrey, who is an executive director of the Sero Project, an organization that fights the criminalization of people with H.I.V., said that until recently, she didn’t worry much about what it would be like to get AIDS. “I think about stigma more than I think about the physical health issue,” she said. But because she lives in Florida, that sense of safety came into question this month. Some of her peers found themselves unexpectedly without coverage for the H.I.V. drugs that keep them alive.