If any airline were to enter Chapter 7 bankruptcy (as opposed to Chapter 11), it could potentially destroy a frequent-flyer program. (Didn't this happen to Midway Airlines?)

But as for an airline entering Chapter 11 and emerging under the same brand name, same general structure, etc. but without an FF program - that seems like such a death sentence that the creditors would throw and even larger hissyfit than the travelers.

If a major carrier like AA or DL were to cancel their FF program outside of bankruptcy proceedings, well, they'd quickly become very familiar with those proceedings. It would be devastating to those airlines and the economies of the cities in which they have their hubs to commit such a suicidal move.