Since they are goyim, we apply their law. This is an area where everyone would hold the Dina Malchusa Dina applies to goyim.
When the creditor sues the debtor, the debtor has a way of saying that the evil third party is really at fault and should pay the claim. It turns out that most legal system find a way to deal with the situation, since it is quite common. What is usual is that the evil third party may be insolvent (happens to evil tortfeasors a lot), though the debtor probably has a way to declare bankruptcy (which would leave the creditor going after the debtor’s debtors such as the evil third party).
If the case involves goyim, let us hope they have Jewish lawyers, who on taking over all sides’ property (that is what lawyers do) will support our tasadakos.