Professionals for finding housing for elderly on medicaid?

Are there services or people that you can hire to help navigate the maze of NYC housing for elderly (77M) on medicaid who is staying with a relative?

He has a social worker due for mental health issues, but they just provided lists of housing options and aren't much help with housing. Most places on that list are only for homeless people, don't return calls, or say the waitlist is literally 10 years.

They've applied to several supportive housing options and been turned down by some assisted living facilities, possibly because he has a severe mental health diagnosis though is stable/not disruptive. He has home help 3x week for an hour, otherwise cares for himself. He possibly has minor memory problems from a stroke, in case that's relevant.