Bankruptcy doesn't mean failure for large airlines. The shareholders get wiped out and bondholders take a haircut but the airplanes keep flying during the bankruptcy resolution so it's fine.
Why would an airline be too big to fail? They don't have counterparty risk like banks.
The airline would go bankrupt, the shareholders would lose their investment, the bondholders would own the new corp, and perhaps the aircraft fleet would get a new livery.