I'm not aware of how other services handle this, but google hands you "Backup Codes" that you can use when you don't have your phone. Google recommends to keep them in your wallet, but I keep them safe on lastpass, which helps when you are without both your phone and wallet.

I think they will make you go through the account reset sequence just like when you lose your password.

Assuming you are using SMS, can't you just get a new phone and port the number over?