This just backs up why I think Finland's recent move[1] to give every citizen a basic salary is the way forward.
You'd then give everyone that basic level of security and enable them to progress in life. Yes there are potential flaws with the Finnish scheme (some people on benefits may ultimately lose out, and millionaires getting the same amount as poor people) - but crucially it would probably stop most, if not all, of cases like this, where someone can't escape the pull of homelessness even with opportunity there.
1 - http://www.msn.com/en-us/news/world/finland-plans-to-give-ev...