“Effective immediately, John Smith has resigned to pursue other opportunities.”
No doubt your organization has its own version of this email. (Fun fact, at a previous employer we called it the POO message for someone who was said to be "Pursuing Other Opportunities.") In fact, if you work in HR, odds are pretty good that you've sent this email yourself more than once. It’s typically sent when your company doesn’t really want to get in to the details as to why someone is no longer with the company. There are lots of reasons that people leave the company and you’d rather not go in to it, but the most important is when you've finally fired someone for harassment.