That is a good question. I don't have any of these kinds of cards to worry about such a thing but I will look into it for you. If I find anything, I will report back!
From what I read, some will be transfer over to another holder or they will be dropped. So in other words, because of the bankruptcy, you will lose out on your miles, perks, and so on. Glad I never signed up for one of these cards!
I don't think any places closed yet, at least not that I am aware of. I am sure they will announce what will happen if/when the time comes so don't worry too much about it.
Last I heard, the airlines will be fine, at lease the major ones that offer airline credit and have agreements with credit companies. Nothing to worry about until the news hits about them filing.
That is the most recent story on the subject and it was from the beginning of June. Nothing new has been said but you can at least get an idea of what could happen.