I think updating the ToS would be part of it and a plugin that allows an admin to delete a user + all their posts / threads would suffice in the context of a forum? It's been ages since I last used PunBB so maybe also delete all their private messages as well. If someone else quoted them it's slightly trickier cause that's someone else's post, but at this point you could tell them they would have to contact you to remove any other posts. I have my suspicion it's not very common for people to ask to be obliterated from online forums having been a user in many for years, it's more common for them to merely abandon their accounts.

Again though, the concerns are real, and I wish I had a better answer other than "don't worry, it's highly unlikely anything bad will happen."