Homeless are, by definition, houseless. Countless houseless folks in the Bay area are homeless, even though they may be working.
Some years ago, one of the engineering grads I hired came from outside the Bay area. We paid him reasonably well, gave him a hotel room for a couple of weeks (or was that month), and suggested he start looking for a place to rent. I'd ask him almost daily how his search was going, and he'd always say that he couldn't find anything he could afford, nor could he find a roommate to share the cost. Well past the hotel time, it occurred to me to ask where he was living in the meantime. "In my car, parked at different shopping malls" was the answer.
I was horrified, and had several employees and my wife looking for somewhere for him to live. IIRC one employee put her hand up and said "I have a spare room". During this search, my admin told me about folks in San Jose renting out areas on the floor of their family room. An area just big enough for a sleeping bag cost $300, no use of cooking facilities or bathroom, and they had to get out first thing in the morning. That was 20 years ago, and I can't imagine what it would be today.