While you shouldn't move out of the country because you're in debt, there are times when you can't help it. For example, if your job takes you out of the country and you have built up some debt, the situation is unavoidable. What you do about it is up to you, but you have several options.
You have the option of continuing to pay the debt, of course. If you decide that you want to honour your agreement with the lenders, you simply contact them and explain the situation. In some instances, they'll work with you to set up another bank account that can be used solely to pay off the debt. This doesn't always work, however, especially if the country you're moving to doesn't have the best banking system. If your new country of residence doesn't have that option available, you might need to set up a bank account with friends or relatives to handle the debt.
If you decide not to pay your debt, you need to consider the ramifications. While you might not think that you're ever coming back to the United States, circumstances could change, forcing you to return. If you do return, you probably will have ruined your credit. However, if you decide that is the route you're taking, you should close your bank accounts that are still in the United States. That way, if there is a judgment against you, your bank accounts cannot be touched.
Even if you move out of the country, the lender can seek judgment against you. Although you might have moved to Singapore, for example, if the debt was incurred in New York state, the lender can file suit in a court in New York. If you do not show up and the court finds in favour of the lender, any assets remaining behind can be seized. In addition, if the company you work for is a United States-based company and a judgment is found against you, you might find your wages garnisheed.
If you leave the country and you owe money, the odds are in your favour that the lender will not come after you for repayment. There are two reasons for this. The first is that there are no treaties in which a debt can be enforced. If a local court in the country decides it wants to work with the lender, that is another matter entirely, since you would be subject to local enforcement. The second reason that a company won't come after you is because, in most cases, it would be simply too expensive to prosecute a debt in a foreign country.