Can you not just block harassers on facebook? I never use the thing (or Twitter) so I have no idea, but I cannot imagine such services becoming popular without an ignore list.

The other alternative is that famous people are being harassed. In which case... well... that happens to famous people in real life too. It doesn't matter if you are online, once you have fame, your life is going to be harassment anywhere. You just need to make a sudonym personal account and not present yourself publicly on forums like facebook or twitter, and only share your new handles with people you trust.