“Not only is there decreased capacity, because Bellevue and Coney Island are off line,” Dr. Kolodny added, “but there’s increased demand because the storm or the loss of their residence has been a stressor for mental illness.”

The storm battered a mental health system that still relies heavily on private nursing homes and substandard adult homes to house people with mental illness. Such institutions have a sordid history of neglect and exploitation, and the courts have repeatedly found that their overuse by the state isolated thousands of people in violation of the Americans With Disabilities Act.

Plans are under way to increase supportive housing — dwellings where mentally ill people can live relatively independently, with support services. But even before Hurricane Sandy, the expansion fell far short of demand.

The storm underscored the fragility of the system. Many disabled evacuees who were sent first to makeshift school shelters lost access to the psychiatric medications that kept their symptoms at bay, Dr. Kolodny said. Even those lucky enough to have the drugs they need are at greater risk of relapse as they experience crowded living conditions. “If they’re now sleeping in a gym with 100 people, that can tip them over the edge and start making them really paranoid,” he said.

On Staten Island, where the chief of psychiatry at Richmond University Medical Center says psychiatric resources have been stretched to the limit, clergy members report that mentally ill people transferred to a large adult home in New Brighton from one that was washed away in Far Rockaway, Queens, are now showing up at church rectories, begging for socks and underwear.

“It’s heartbreaking, because they just found us by chance,” said Margaret Moschetto, a missionary at the Church of Assumption-St. Paul in New Brighton. “They were just walking around the neighborhood. They really didn’t know where they were.”

Ana Marengo, a spokeswoman for the Health and Hospitals Corporation, which operates city’s public hospitals, would not answer questions about where emotionally disturbed people were being taken for evaluation in the absence of Bellevue and Coney Island, which were not expected to reopen before February. Nor would she say where the city had transferred hundreds of psychiatric patients when the two hospitals were evacuated, or how many outpatients had been lost to follow-up.