It'll be tied to a Microsoft account. Whether that person uses that is another question. Many websites now don't need an email to use, just a phone number. So i think younger people would easily not notice. I imagine like google accounts you can, "sign out all accounts", which would mean the Xbox too.
Depends if you care for those games. I'd play them while you can, but certainly wouldn't add any Gold membership or buy any games on that account for fear of being signed out permanently.