This is also now my experience with the homeless problem in my latest city. I probably got lucky with the previous city, as this one has only 28k people, and 6k of them are criminals. Homeless everywhere, not moving into any cheap houses, no amount of welfare or anything is solving this problem. Police aren't patrolling, my prison is sitting there only a quarter full, while there are well over 1k sentenced criminals in the city (why aren't they in the prison?), and I'm even finding that the city ordinance is doing nothing to rehabilitiate criminals in time.
Are homeless treated automatically as criminals? Is this preventing them from integrating? I'm curious to see what's going on here and how its solved.