That said, there are certainly people who live with family or take on roommates that otherwise would prefer to live independently due to high rents. So it is an issue. But rents declining a bit, or even a lot, wouldn't put a dent in homelessness.
https://www.vox.com/the-goods/2018/12/14/18131047/homelessne...
Interviews of homeless people, at least in some West Coast cities, indicate that drug addiction is perhaps the single biggest contributor to homelessness.
The supply of housing needs to drastically increase in housing-constrained places that suffer from homelessness. That means fewer zoning regulations, fewer environmental regulations, stronger rights of property owners to develop and sell or rent their property for what the market will bear, allowing "poorer" housing (like the boarding houses that Yglesias's article discusses), and so on and so forth. But you also need to convince the public that the people they see strung up on the street can be good neighbors; otherwise none of that policy change would happen. So we must also address drug addiction.