I don't think that it's the government's fault why they are homeless. Maybe a part of it (not being able to accommodate everyone). The more at fault is the person himself or herself because they won't land there if it weren't probably for their bad decisions. If you grew up being in poverty, it would be hard to get away with it, but if you do good to people, you would eventually get out of it.
This is not always true if most of the population is poor and there are not many chances to get out of it then you may end being poor despite your best efforts.
More precisely, they just do not give a chance that they could provide themselves normally. Just others it will be unprofitable.