If you marry someone who owes back taxes and you file jointly then you become responsible for the persons back taxes.
But if you file separately on your income taxes then you don't become responsible for your spouses back taxes after you get married.
If you do or did file your income taxes jointly then you can file the 8739 form which will allows you to retain your own refund even when you did file the taxes jointly.
But if your spouse owes back taxes then it's best to file separately and not jointly to avoid any trouble.