> How do you know people don't become mentally ill or homeless after losing their home

Because a substantial portion already have a history of mental problems before they became homeless, and typically they find themselves homeless because they reach adulthood and thus their primary caretaker either can't or won't be able to keep them off the streets. I personally know a couple of homeless individials that suffered from schizophrenia who found thenselves on the streets after their patents passed away.