A group called “Manila Principles” has developed a form for service providers to use to inform users when the providers get a takedown request for any reason. The primary usefulness for the form is apparently related to situations other than just copyright infringement. The link for the form is here. Notification requirements are defined by law for copyright under the DMCA, but not for other TOS violations or potential "torts".
A group called Online Censorship explains how to appeal here.
Jeremy Malcolm of Electronic Frontier Foundation has a story explaining the use of these facilities here.
The main issue is whether users are properly notified when there is a complaint about content they have posted, and whether they can rebut (especially in areas outside of copyright).
I’ve been contacted only a very few times over 18 years directly by people. In two or three cases, the personal circumstances were quite unusual and unlikely to recur with anyone else. In one case, there was a misleadingly worded statement in a Blogger movie review of a controversial documentary, an assertion which might have been misconstrued in a way harmful to a real person depicted in the film.