Yes it is absolutely the case as I have seen in the thirty years I have volunteered with homeless shelters.
Typically it is PTSD that sometimes leads to violent responses that makes these people want to be unhoused. We have a lot of vets in my country, The USA, who aren’t getting the mental health care they need. Some of these people are on the streets because they do not trust themselves around loved ones.
So, you get my point. It isn’t just a desire to be on the street because they think it’s cool and fun.