In the US they call it conservativeship when an adult can gain legal custody for another adult or family member. Usually they have to be pretty incapacitated though, and a judge has to rule on it, that the person in question can no longer make decisions for themsleves. This law mostly applies to people with mental illness or to elderly people.
They threatened this against me while I was locked up though. I have never talked to another person that it was successfully used against them, usually the threats are enough. From my experience, I would say it's not the living on the strets, or having no money or any of that which keeps kids from leaving as much as the parents sometimes make it very clear if they leave the program at 18 they are disowned. The programs teach parents to make it clear they will stop loving the kid if they walk out, they call it tough love, I call it betrayal, the kind that can never be forgotten.
