Make them put everything in writing all the time. My boss knows that my response to requests is along the lines of "Send me the details in an email and I will see what I can do". Anything that I don't have an email for has a 50% chance of being legitimately forgotten even if I want to do it.
I hear you! Qe have a person who is delete happy. We have a common email i box with CONTRACTS and similar things that she deletes. I have to retrieve from trash when i have time. Utterly senseless.
I have been in meetings where a customer was grumbling I hadn't done something and before I could say anything she asked "did you email him"? They hadn't and I didn't need to defend not doing the work, I just sat there while boss explained that they aren't special and everybody has to email requests