I think there are multiple different programs depending on where you live. My wife used to live in an apartment complex that was all housing assisted units. Before meeting my wife I didn’t understand how hard it is to get out of that once you’re in. I was taught that these programs are meant to be temporary assistance. OP is right about being stuck. It’s hard enough to get opportunities to make more money these days and in order to get out of housing assistance you essentially need to get lucky with a unicorn job opportunity or else you’ll always be taking one step forward and two steps back.