There are literally millions of people who want jobs. The jobs were all made obsolete by Silicon Valley. The safety net was shredded by Silicon Valley-style neoliberal ethics based on Ayn Rand.
If someone offered them a rat race job and they had the appropriate education, cultural norms, social skills, and were mentally healthy, they would take it.
People don't choose to be homeless. It may be the best option available to them, but that doens't mean they chose it, it means they have very very few options. Their opportunity is limited by the rich people pushing austerity and gutting basic humanitarian services.
A particularly common combination was a health problem followed by foreclosure.
It has been 20 years, but I have seen no reason to doubt that the same pattern would be largely true today.
It's not about if someone wants to be homeless, if there is a simple choice between shelter and homeless, people will always prefer shelter. But if the choice is between working hard with a shelter, and live carefree and homeless, the answer will not be so clear.