CO went into bankruptcy twice, the last time I think in 1993. America West has been there, too.
United went in Dec 2002.
If it is Chapter 11, you have nothing to fear. They will continue just as they are.
Remember, Ch 11 is Reorganization. A breathing space, if you will, that lets the airline renegotiate certain contracts. For example, leases on aircraft, contracts for hotels for crew, catering, and airport leases.
They will then go to the employees for "give backs." If they cannot get the crew/employees to give back enough, they can then go to court and ask the court to nullify the existing labor contracts.
They then have something like 60 days to negotiate with the labor groups. Then the newly-proposed contracts are voted on. If they are rejected, basically the labor group is on strike.
This is different than Eastern. The law was changed after that.
The first thing they will do in Ch. 11, if they follow past treands, is go to court and ask the judge to allow them to continue certain contracts, such as the discounts they give the big corporations who have signed agreements with them, as well as the frequent flyer programs.
Congress passed a law a few years ago that says if an airline declares Ch 7 ( two have done that in the past five years ), then the remaining carriers have to take their tickets on a stand-by basis, with no charge over $25 to do it. The airlines are only obligated to provide service to like airports. For example, Atlanta to San Francisco, UA and AA could accept, even if it is with a change of planes along the way. But you cannot take the ATL-SFO ticket and try to use it from Charlotte, or to San Diego.
The airlines can put in special fares for up to 30 days ( maybe 60, I don't remember ), and charge you extra for a confirmed seat. You have to prove you have a ticket on the defunct airline, purchased at least the day before they ceased flying.
I think this just applies to ARC carriers, not Southwest or Jet Blue, as they aren't ARC and don't cooperate with other airlines.
My personal opinion ( I'm between jobs at United ) is that Delta isn't going anywhere. Ch 11 is a possibility, but I just don't see Ch 7 in their future.
Don't count on bankruptcy court to give you your money back in Ch 7. If they liquidate, there won't be enough to go around to all ticket holders.
And your credit card will only refund you within 60 days of purchase.