Do I have to pay debt if I move to another country?
You didn't mention how long you haven't pay back the debt. However, if your debt is statute barred, the creditor cannot go to the court to get the money from you. But they can still chase you for the money.
If you don't pay your credit card debt and a lawsuit is filed before you leave the country, the case will be forwarded to the next level in your absence. However, the lawsuit can't force you to pay off the debt once you're settled in another country.
But creditors may pick up the trail of yours and go after you. Likewise, if you go overseas but continue working for a U.S.-based company, there's a chance that your wages could be garnished as per the court rules.