The Witness Protection Program is not under jurisdiction of the F.B.I. It's a part of the U.S. Marshals. And it's actually the Witness Security Program.
Members can only join under extreme circumstances in cases in which their life is in serious danger.
Though physical alterations such as plastic surgery are done, they are very rare. Most witnesses simply change their name, either their last or both first and last. It depends on the case.