How on earth did the USA survive Edsel going under?
Seriously, though, loan guarantees by the govt. would have made a private sector style bankruptcy work. It's worked numerous times in the past, even with bank sector collapses in progress.
People either forget or ignore the fact that 9/11 was a major hit to a number of our banks and markets. After the terrorists used airliners as bombs, nobody wanted to fly for business or pleasure. The insurance companies didn't want to insure airline flights. The airlines and companies that built airplanes or suppliers of anything related all suffered greatly. A bailout ensued - $15B, $5B of direct aid and $10B in loan guarantees.
Since 9/11/01, airlines have filed for reorganization (bankruptcy) FORTY times.