Not necessarily. Some of the companies are structured such that they don't own the patent, just certain rights to it. Basically they sue on behalf of someone else which both reduces the risk and also allows the patent owner to claim that they're not the one behind the suit.

I'd imagine that those rights would just be tied up so they weren't transferable (so if the company did go under they would no longer be an asset) and that this structure would become the norm.

What you'd need to do is have the suing company stump up the money in advance into some sort of escrow account (or some other mechanism for proving they can pay).