That's true they're more likely to be poor after they've become drug addicted and homeless, but they are also more likely to be poor BEFORE they become drug addicted and homeless.
Evidence? Studies? I can see that to some degree because the state doesn't afford the necessary services while rich people can pay out of pocket to seek treatment for their relatives. But since the state refuses to admit people for mental health issues, then who exactly is exacerbating the problem?