Groups with NUL operator are not displayed on Activities tab, and so cannot be edited/assigned actions.
Existing groups with activities where the user changes the group operator to NUL will present a confirmation dialog warning that the group's activities will be deleted and confirming intent. An affirmative response causes the group's activities to be deleted.
A group that uses the NUL operator can still be assigned actions in Activities, but there is no way for these activities to run.