I don't know and I don't think it matters. What they have purchased is the right to sue for any copyright violation and to be the plaintiffs (thus insulating the newspapers from any problems that might arise if they were to lose the lawsuit and be countersued for some tort, like abuse of process).
This kind of practice of law appears to me to be quite similar to a law firm that used to exist in California called the "Trevor Law Group".
The tactics of Righthaven appear to be almost identical to those of the Trevor Law Group and their abuse of the legal system appears to be at least as eggregious.
Ultimately all the lawyers at the Trevor Law Group were disbarred.
We can only hope that the same fate awaits the lawyers at Righthaven.
If this works like the East Texas patent trolls, they have created an LLC with no assets just for the lawsuits. If they win, the company pays the attorneys and the original owner's cut. If they lose on a countersuit, there are no assets to surrender. Of course it being an empty LLC, there's nothing really to countersue over.
BTW, the Texas patent trolls often go further, creating a new LLC for each separate lawsuit, dissolving it after each case is concluded. It's worth it because they're going up against big companies and aim to reap millions from each suit. Unfortunately, I haven't even heard a rumor over disbarrment among those attorneys.