Most of them are in a better state then alone in a strange city, with nothing but the clothes on their back. They often have jobs, and may be living on couches or in a car, or have a bank account, or social support (Not enough to keep them in a home, but something.)
The homeless that are sleeping rough for 9 months tend to stay homeless. It is a horrible way to live, and it breaks you down really fast.
because they find a home. Think about how many people in the US are living hand-to-mouth, where any disruption can cause them to fall behind on rent. Those people make up the majority of people who have been homeless recently. They are homeless for the time it takes them to save up a deposit and find a place to live.
You don't end up homeless when you have someone to call to come and get you. You end up homeless when you've burned through that bridge.