Riker's Island in NYC is a prison hospital - all of its inmate are diagnosed with mental illnesses as are the prisoners at Skyview Psychiatric Prison Unit, Texas; Bellevue Prison Ward, NYS; California Medical Facility in Vacaville, CA; Federal Medical Center, Carswell, Fort Worth, Texas; Federal Medical Center, Devens, Devens, Massachusetts; Federal Medical Center, Fort Worth, Fort Worth, Texas; Federal Medical Center, Lexington, Lexington, Kentucky; Federal Medical Center, Rochester, Rochester, Minnesota. These are all places where prisoners with psychiatric diagnosis are held in separate wards: Bronx Psychiatric Center, NY; Sing Sing, Westchester; The Center for Forensic Psychiatry Correctional Facility, Ann Arbor, MI; New Hampshire Hospital; Eastern State Hospital, Forensic Division, VA; - just to name a few.
As for people with other disabilities - they are housed with the typical prison population - and not always with the needed accommodation to lead a dignified life - even for a prisoner.