Housing First for chronically homeless people is associated with decreased jail time.

A UW study examined criminal history as a predictor of housing retention and subsequent jail time for chronically homeless people housed in a DESC Housing First program. As with the other study, criminal history did not predict housing failure. This study also showed that prior criminal activity while homeless is predominantly minor, and that subsequent bookings into jail and days in jail decrease substantially. See:

Exposure to Project-based Housing First is Associated with Reduced Jail Time and Bookings – International Journal of Drug Policy (Volume 24 | Issue 4, July 2013)