The recently added functionality to have members join and leave groups on membership sites is fantastic.

It comes the option to have triggers fire when a request to join a group is requested, approved or declined. That takes care of the whole scenario when members enter a group.

If a member leaves a group, it could be relevant to also do automated stuff like remove badges, tags, start automations or send emails. So i suggest adding a trigger "Member leaves group" and have that fire when a member manually leaves a group.