I once worked with a guy that lived in the cab of a small pickup truck. He had two jobs and was working to pay off his loan on a small ranch he had bought in Wyoming. His goal was to someday have his loans under control and then go back to his ranch to live. When I worked with him he was operating a machine on second shift in computer industry company. I was then a tester in the same building. His other job was as a janitor at the university. When not working he would drive to a lighted parking lot and shut down. He was wrapped in heavy coats and did without heat in the winter.
I did drive up to his ranch in Wyoming with my daughter to see an old Studebaker car laying on his property. He had a home on that property but no industries to work for. So he was about 100 miles south working. He was really satisfying his wants and living on the streets to make it happen.
Many others have divorces, alcoholism or drugs, unwilling to live in what we call normal society, bums, fugitives, whatever. Lots do go to the shelters for food and a place to sleep at night. They then have to leave during the day so the shelter can clean up and prepare for the next evening. For many, non of the welfare will do the job as many just don't want the restrictions and confinement. That includes both men and women. Giving them pocket money just opens up the ability for many to buy alcohol or drugs. Sort of a part of our society that we will have to put up with. Give them a job and pay them. It might work, but if they can not afford or desire to maintain a place to live, what will we do? We can not just jail them or put them into a lock up shelter.
This is 2009 data. the best I could find.
http://www.nationalhomeless.org/factsheets/How_Many.html
On an average night in the 23 cities surveyed, 94 percent of people living on the streets were single adults, 4 percent were part of families and 2 percent were unaccompanied minors. Seventy percent of those in emergency shelters were single adults, 29 percent were part of families and 1 percent were unaccompanied minors. Of those in transitional housing, 43 percent were single adults, 56 percent were part of families, and 1 percent were unaccompanied minors. Those who occupied permanent supportive housing were 60 percent single adults, 39.5 percent were part of families, and .5 percent were unaccompanied minors (U.S. Conference of Mayors, 2008).
.............................
And this is just definitions of who they might be.
https://en.wikipedia.org/wiki/Street_people