We have a related issue:
It is important to notify users that someone added them to group “X” (or removed them, e.g. like facebook does). Otherwise there will be much repeated confusion or manual work for group owner to notify them as PM.
Also it is important to notify the group owners about new/left users (to take timely actions).
On our forum we need to restrict topic creating powers in category “Y” to members of group “X”. Our supporters automatically get added to Patrons group (via Patreon plugin), then we create a dedicated category for their needs (as a reward).
We also create a dedicated group for each of our Patron (so they can invite their staff to post in their dedicated category).
It would be even better if members of a particular group (e.g. Patrons) could create one group themselves, and automatically become the owner of that group.
When someone leaves a group (e.g. stops their support and leaves the Patrons group) the owner of that group (e.g. site admin) would receive a notification and then manually perform some actions (e.g. change permissions per category “Y” or assign a new owner for group “X”).
Update: @sam Sorry for buzzing, but could you take a second look at this request?