Someone wants to send nasty things about me to my Facebook friends and family.
How do I stop them from doing that?
This is an offence in most countries. Report it to the relevant authorities.
There's no technical way for you to stop that (if they're using their own account to send the messages). However, if what they are doing constitutes harrassment, you can report it to FaceBook (to have their account suspended) and to the police (for harrrassment, threatening behaviour or whatever the offence is in your country).
you can report it to facebook and they can block the account, but that person can open a new account and repat the action
Can I forward threatening email abuse to Facebook
How do I report harassment or abuse on Facebook if I don't have an account?
What should I do if I'm being bullied, harassed or attacked by someone on Facebook?