That depends: in some cases it appears that they've tried things as blazen as having a shell company which licenses the rights to sue for a patent but doesn't actually own it. If the shell goes bankrupt, the only “asset” is that right to sue, not the actual patent, and the people involved are free to simply try again later.

If you haven't looked at this before, This American Life had a two part series with a good general examination of the system – spurred by a troll running around suing everyone who podcasts:

http://www.thisamericanlife.org/radio-archives/episode/441/w... http://www.thisamericanlife.org/radio-archives/episode/496/w...

> Also, would it be possible to seek legal expenses from the shell corporation's creditors?

That's a really important question. The assumption has been no but there have been attempts to try RICO cases[1] and it sounds like the entire legal climate is getting more sympathetic to the idea that what we're seeing is extortion, pure and simple. Most of the legislation floating around Congress at least made some attempt to deal with this part of the problem but, of course, none of that counts until something is actually close to passing.

1. e.g. yesterday's story: http://arstechnica.com/tech-policy/2013/11/findthebest-destr...