Perhaps the answer is to just keep going more dense, if one’s position is that within a country, anyone is allowed to live anywhere, either via their own means or government assistance. But I do not see that being politically popular with many, and I can envision a few feasibility concerns with that approach.
Another option is that the location where you get a social safety net is not guaranteed, and so desirable land is distributed according to one’s wealth (which I know is highly dependent on one’s ancestry).
Homeless people move to places with mild winters, because they don't see housing as an attainable goal. Maybe they'd move somewhere with free housing -- or maybe they'd assume that any such program wouldn't survive an election cycle, so would rather stay put than get their hopes up.
But my point is is there an obligation for society to not have to make people move if the economic conditions change and labor supply and demand curves move? What are the long term effects of these incentive structures?