In theory, couldn't people unable to find housing where they currently are apply for jobs in states/cities where housing is cheaper, thus achieving a buyer and seller equilibrium? What policy changes could facilitate this kind of mobility?
There are 2 limiting factor that I've seen.
First is knowledge. If we're talking about the homeless or other low income workers, we're probably not talking about highly skilled workers. For the low skilled workforce, there are decidedly fewer options available for learning about job openings. So, that's probably the first thing that would need some kind of change - an easier way to learn about low skilled work in other states.
Second is cost of moving. I'm always surprised by the number of people who don't take jobs in other states because they cannot afford the move. It's the cost of getting your stuff organized, packed, etc. Plus the cost of a new place to live, usually a security deposit, first and last month's rent. Then the usual 2-4 weeks before you get your first paycheck from the new job. These costs are bigger burdens the lower down the income ladder you are.
So, that's another policy change. There used to be some work related moving deductions (I don't know if they still exist, haven't looked) but, as with all deductions, you have to spend the money to get the deduction...which isn't very helpful if you don't have the money in the first place.
Some method for people to move for work where they can defray the cost of moving would have to be the next policy change.
