How can I find a place for my mother-in-law to live on just social security income?

Jeannegibbs nailed it. Please do as she suggested. Subsidized housing is local. The intent is to make housing affordable for people, many of them elderly, who don't have the ability to pay rent. Social Services should be able to help give you direction. Also, as Jeanne said, if your mother is not on Medicaid she would likely qualify. Contact the social services in your mother's county.
Take care,
Carol

OSCARMEYER, I suggest you start by contacting Social Services in your mother's county. They are experts at what is available under all kinds of circumstances. If your mother is able to live independently a likely option is subsidized senior housing. Where does your mother live now? Sometimes there is a waiting list, but Social Services can help with that.

Does your mother need help because of health issues? Applying for Medicaid would be appropriate. Again, Social Services can steer her in the right direction.

Good luck!