This is not supposed to happen.
The Foreign Sovereign Immunities Act of 1976, which exempts sovereign nations from litigation, was enacted to avoid this. It prevents United States courts from attaching the property of foreign countries, a reason you don’t see American creditors seizing Argentine frigates in New York harbor. But in the suit by Elliott and Aurelius, the courts sidestepped this act by ruling that their decision reflected how Argentina should act, without requiring it to pay. If Argentina decides not to pay the new debt, it does not have to pay the old debt. Still, the spirit of the act seems violated. And it is bad news when United States judges are seen as controlling the destinies of foreign countries.
Steven Davidoff provides an absolutely excellent one-stop primer on Elliott vs Argentina