[bluGill]

Most homeless have mental issues. Minnesota has a good welfare system. However the cold in MN means that those who generally don't trust government (meaning that they will run away from any help the government tries to give unless restrained in an often inhuman way) either freeze to death or make their way south. Thus the poor in MN have a house of some sort. There are a few who migrate north for the summer and back south for winter.

No amount of safety net helps when your mental illness makes escaping the notice of the safety net a priority. It is a hard problem and I don't think anyone has a good solution.