I don't have it on hand at the moment, but I think I saw something about how the victims of those lawsuits didn't actually end up paying. Might have been related to bankruptcy, and certain things being non-enforceable. Basically the RIAA cottoned on to it not being worth their time and money to ruin their public image for little to no return.

Edit: Still can't find it, but did find this EFF article covering a bunch of people who apparently settled for some amount. Haven't followed up on the people who took things to court yet. https://www.eff.org/wp/riaa-v-people-five-years-later

Edit 1: I think it might have just been a high-profile case or two that escaped paying, it seems there were oodles of people who did pay based on the EFF article.