A combination of direct cash assistance and mental healthcare would go a long way towards eliminating homelessness. I have not performed the study, but suspect

A combination of direct cash assistance and mental healthcare would go a long way towards eliminating homelessness. I have not performed the study, but suspect that in the long run this would be less costly than the current system since it's much easier to maintain mental health when you have housing. I would expect most of the participants to eventually integrate back into society and no longer be dependent on the subsidies for basic needs.