It depends on the type of bankruptcy: in a Chapter 11 reorganization the airline keeps flying and your miles almost always survive, but in a Chapter 7 liquidation the airline shuts down and miles usually become worthless. Mergers almost always preserve your miles by converting them into the surviving airline's program.
Most airline bankruptcies are not the end of the world for your miles. It comes down to which kind of bankruptcy the airline files. Chapter 11 is a reorganization, where the airline keeps operating while it fixes its finances. Chapter 7 is a full liquidation, where the airline shuts down and sells off what it owns. Your miles behave very differently in each case.
Most large US airlines that have filed for bankruptcy did it under Chapter 11, and they kept flying the whole time. Delta, United, Northwest, US Airways, and American have all been through it and came out the other side with their loyalty programs intact. Frequent flyer programs are actually one of the most valuable parts of an airline, because the airline sells miles to banks and credit card partners for real cash. That gives it every reason to keep the program running and keep members happy.
The catch is value, not survival. Even when your miles stick around, the airline can raise award prices or cut availability, so the same trip may cost more miles than it used to.
Chapter 7 is the scenario to worry about. If an airline stops flying and liquidates, its miles can become worthless almost overnight. Legally, mileage holders are treated as unsecured creditors, which means you sit near the back of the line when assets get paid out, usually behind banks, bondholders, and employees. In practice, members of fully shut-down carriers have often received little or nothing for unused miles. The good news is that outright liquidation is far less common than reorganization for major carriers.
A lot of airlines emerge from Chapter 11 and then merge with a stronger competitor. In those deals, your miles almost always come along. When Northwest merged into Delta, WorldPerks miles converted to Delta SkyMiles at one to one. When American and US Airways combined, both programs merged under the AAdvantage name and Dividend Miles balances carried over at one to one. Conversions are not always exactly even, but a merger is generally good news for your balance, not a reason to panic.
Do not let miles pile up unused, especially with a smaller or financially shaky airline. If you hear bankruptcy news, stay calm and check whether it is Chapter 11 or Chapter 7. For Chapter 11 you usually have time, though booking an award sooner protects you from devaluation. For Chapter 7 or a sudden shutdown, act fast or assume the miles are gone. Holding miles in a big global program, or in transferable credit card points, also spreads your risk across more than one airline.
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