Assuming it's not a work-for-hire, copyright remains with the author. But the specific publication rights that the author has licenced to the publisher are part of the publisher's assets, that can be sold off to raise money to pay off the debts. (This is US law.)

If the publisher simply decides to close up shop, then they can do whatever they like with the company property, including handing publication rights back to the author -- and in fact the author can demand that they do so, *if* there's a reversion clause in the contract governing what happens when the publisher ceases to publish the book. But if they declare bankruptcy, all their assets are sold off, and that includes the specific publication rights they've bought. Which, as mentioned in that post, is another good reason to not allow them to take any of the rights they have no real chance of exploiting (it's common for publishers to try to grab the film rights, for example).

There was a long discussion about various things including this a few years ago at Making Light, after Teresa offered up an example of Very Bad Advice that was being promoted at the message board of a well-known vanity press:
http://nielsenhayden.com/makinglight/archives/002703.html
Of particular note are the comments at 4, 44, 46 and 49.