If not for my mom somehow knowing about accessible housing less than five minutes from home, I feel like we would have really struggled finding housing. The building where I live (and several others like it within my state) were designed for adults with physical disabilities, and to qualify to live here, we must be low-income and disabled. Since those two things are pretty synonymous these days, that is not a problem.
I'd say availability is a problem. Because each building is rather small, and usually residents live here for long periods of time, it took several months for one to open up for us. Even then, it was a one-bedroom. It took several more years for this 2-bedroom to open up as only a fourth of the apartments are 2-bedrooms. One is lived in by the apartment caretakers. Also, this particular accessible housing looks like it's only within my state.
I would have never even known where to look in the first place to know how to find accessible housing. It's not something I've ever seen advertised - so we have helped a friend of a friend find housing after she became disabled. It seems we (the disabled community) are all we have and we have to help each other out, and spread helpful information around. Otherwise, we would never find it.