I've known homeless people, and they were indeed refused support by their family. Family in this case was dad, who was a ornery SOB and disowned his son for going to university instead of working on the farm. Nice.
The son was a slightly geeky maths student. He screwed up some paperwork and didn't get any housing allocated by the university one term. He slept on a mate's floor while trying to sort it out. Then he felt the mate might be getting fed up with him, so he lied and pretended he had somewhere.
Then he started sleeping during the day in the computer lab (how I met him) and just wandering around at night. This didn't do his grades much good, and he dropped off the course.
Once you've been sleeping rough for a very short space of time your mental health nosedives. Asking anyone for help becomes very hard - it's a challenge just keeping basically clean and fed. Note that he had some money (unemployment benefit), just nowhere to live. He could afford to eat, but without access to a kitchen he either ate only cold food, or had to buy (relatively expensive) take-away food. As a single young male you are not on the top of the queue to be housed by the state.
In the end he escaped, and last I met him he had a job, house and girlfriend. But I've seen how someone can become homeless, it doesn't take much, and once it begins it's very hard to stop.