The liberators figured that these unhinged people would have the good sense to seek treatment as outpatients. Because they went along with the whole scheme to save money. Closing the mental hospitals was a revenue windfall, so they turned a blind eye. The fact is, there are some legitimate government functions. Amitai Etzioni, in perhaps the only brief and interesting thing he's ever said, observed long ago that children do not fit the libertarian paradigm.
Government needs to make mature decisions about what to do with damaged people.
Letting them die of frostbite in the name of liberty or Clintonian compassion is not a mature decision. I'm sure Giuliani's plan for the homeless has its faults. But it is a plan. It recognizes unpleasant facts and deals with them. It doesn't make the people living on the streets into cuddly heroes and it doesn't make them Jesus either.