The problem here is a doctrine known as "champerty" - something that Elliott was actually found guilty of, once, in a ruling which was overturned on appeal. The problem is that it's considered "intermeddling" to invest in someone else's lawsuit (doncha just love these legal terms). So the solution is to buy litigable securities - often defaulted bonds or loans - for one's own account, on the cheap. Thus does an investor become a genuine plaintiff in good standing, with a legal claim enforceable by dint of the loan documentation.
Historically, then, lawsuits-as-an-asset-class have been largely confined to the "vulture" end of the distressed-debt spectrum. But where there's a large amount of profit, you can be sure that some hedge fund somewhere will find a way to get in on the act. And I wouldn't be at all surprised to see hedge-funds finding some way to invest in torts and class-action suits, down the line. Maybe UK hedge funds MKM Longboat and Juridica will be the first to do so.