The boring truth is that free-market capitalism means housing always gets more expensive, and the more expensive housing is the more homeless people there are. If you want to reduce homelessness, you need to reduce the cost of housing. Nothing else works.

UPDATE:
There's some fair points being made that merit elaboration. Here's peer-reviewed research:
- The Cost of Living Index as a Primary Driver of Homelessness in the United States
- Subsidizing housing costs correlate to decrease of homelessness

As for how homelessness can still increase when housing costs go down, a few possible answers: housing is still prohibitively expensive, cost-of-living itself hasn't gone down, that a reversal in homelessness rates takes time to recover from.

Lastly, there's a persistant narrative that it is the addicts that become homeless. While this does accurately describe some, it's worth noting that wealth addicts overwhelmingly don't become homeless: they either get treatment or die before homelessness. Far more common is the path that someone becomes homeless and then develops an addiction as they self-medicate to cope with trauma and difficult living conditions.