It means the troll's shell company, whose only asset is the now-useless patent, is shut down. The parent company isn't touched, nor the thousands of other subsidiaries owned by said parent company.
Deliberately underfunding an LLC is not something that is going to be looked upon kindly, particularly if it's purpose is exactly to get around the law.
Any judge worth his salt would either sanction the hell out of the lawyers involved, or let you go after the parents.
As I mentioned in another reply: How could the judicial system incorporate rules to pierce the corporate veil in such situations and therefore expose the shell company creator(s)? Would something like this help? And what are the cons?