The fact is for the majority of countries in the world, debt is not a crime, so it does not have any affect on travelling. And leaving debts behind, while some may consider a moral issue, is also not a crime; in the majority of countries.
However, what if you move from one country to another country, and still wish to pay any accounts you have in the previous country.
An example may be you move from the UK to the USA, and you have a credit card with a balance in the UK, and other assorted loans.
While in the USA how do you pay these accounts?
Speak To Your Creditors
Talking to those you owe prior to moving is a wise move. They can give you information and details on what is required to pay them from abroad in other countries.
They can provide you with an IBAN number or international banking code to be able to continue your payments. This would be if you were sending payments from outside the UK.
Banking and Exchange Rates
If you move from the UK to the USA and maintain a UK banking account, as long as you have funds being payed into that account, the setting up of a standing order or direct debit can be used to continue making payments.
If you do not maintain a UK bank account, or no longer are having money paid into the account, you can transfer funds into the UK account those various means. One is via Paypal, and another is to use an international banking transfer.
However, we then need to deal with the currency exchange rates.
If your monthly payment to a credit card is £50, you may need to send $70 in order to pay the full payment. Currency exchange rates change on an almost daily basis, and you need to insure you send the correct, and full payment.
As you can see, making payments from one country to another is not as complicated as one may think, but you do need to prepare and do some research. You also need to be aware of currency exchange rates.