Your problem, your story😃.
Just saying you've introduced a character that can best be explained by him having nefarious motives.
The police don't care about homeless people, they'd just pass the buck to social services,who can't deport people either. Their job would be to either find a relative, care home, foster home or, if old enough (16,17), some way of living on his own. Tough luck if he's 18, pretty much on his own. They wouldn't send him to a relative in another country. Well, not since the 1970s , when they stopped sending kids to Australia (and some of those still had living parents).
If he had a criminal record ,& a bad one, think murder or rape to be deported (home secretary) as they'd have to rescind his British citizenship (only if he had dual nationality). If it was that bad , immigration officers in the USA would just refuse entry and send him back to Britain. They wouldn't want him, just as Bangladesh said the Isis bride was our (UK) problem, not theirs even though she could claim citizenship from her grandparents. She's back here now fighting a court case to overturn the revoking of her citizenship.
Non UK citizens can be deported by judges , as part of the sentence for serious crimes.