That was certainly part of the problem in some case, but the overarching issue is that rent increases are outpacing inflation and income - this means that people are forced to devote more and more of their income to rent, and those who are on the cusp of homelessness increasingly fine themselves over the edge financially.
The issue I see, however, is that it is the "free market" causing most of the current increase in homelessness. The issue being that rich people buy up the land in the cities, increasing the cost of housing (both land and the rental costs, particularly as tax rates go up due to increased property valuations). The upper middle class, not being able to afford new homes in the city, move into the suburbs. The middle class, now being priced out of the suburbs, go to the "new suburbs" that are often 30 minutes or more from their work -- meaning that while their housing costs are similar but their transportation costs increase, causing a further strain on their budget. This causes the lower middle class to be completely priced out of the housing market -- anywhere they can afford to buy or rent is so far away that the can't afford to live there.
Some talk about public housing, but everywhere I've seen demand is too high. The last place I lived had at least a year wait time, and that is even if you had priority (such as some type of disability that pushed you higher on the wait list). I don't see how you fix this without methods to override the free market -- and even then that often causes unintended issues.
For example, rent-controlled housing in New York is estimated to have taken 10s of thousands of units off the markets, as owners have decided it costs more to rent the units, in upkeep and other costs, than they will make renting them out at the reduced rate. Some estimates claim 60,000 units are currently empty because owners are no longer renting them.
Other places, like Hawaii, are putting bans on using housing as short-term rental units, that they need to offer long term leases rather than to rent them out to vacationers on AirBnB. I'm not sure how you fix the problem when the rich see real estate as one of the strongest investments -- even buying extra homes to be used as 'vacation' homes that otherwise stand empty -- with the idea that they'll likely be able to sell them in a couple of decades at twice the cost they bought them for.
There is also a real resistance, particularly among homeowners, to creating new high density housing -- particularly "lower income" high density housing. But in most areas, such as a new project for a 20-ish story building in a recently revitalized (and gentrified) neighborhood, that even though it is for luxury housing there is strong opposition to the company trying to build it.
I'm really not sure what "fix" there is, particularly since it will likely cause restrictions on the free market, something Republicans typically strongly oppose, even while they are the ones that appear to be complaining the most about the housing issues.