Slip and fall in a New York prison, or suffer abuse by its guards, and inmates can keep whatever they win in court. But for patients in state-run mental hospitals — people too ill to live on their own and too poor to pay for their care — the state can drain court-awarded damages, effectively deducting the cost of their stays in the very hospitals that failed or abused them. “It’s a Catch-22, isn’t it?” said Leo G. Finucane, the lawyer who represented Mr. Langevin. “I need to go to this facility because I’m sick. But if they hurt me worse, they’re immune.” It is not uncommon for public hospitals to lean hard on patients found to have assets. But New York squeezes patients who sue for injuries more consistently and harder than many other states, according to lawyers and others who represent the mentally ill.