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

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.