What exactly happens to an NDA if the company goes under or is bought out?

You did put in clauses which indicate post-termination time-expiries? Legally there may be some jurisdictional issues but you didn't state what the NDA covered, so some companies expressly write in return of written documents or enjoiners on future ex-exployees. If you can't police the existing NDA, what hope to enforce a future scenario ... which just shows you shouldn't write down anything you can't exercise power over (though lawyers might disagree) either directly or through judicial/administrative means. If there was a law on mind-control, it would be Orwellian 1984 already.

An NDA is, at it's most basic level, an agreement between the company and another party to keep something secret. Agreements a company has entered into may be considered assets in bankruptcy. If someone were to purchase this particular asset of the company that went under, they could be considered a successor in interest to the bankrupt company. Now, you can deal with almost anything within an agreement. As long as it isn't against the law or public policy, and the other party agrees, there's no reason you can't deal with this issue in the terms of the NDA.