If the group is set as private and the mod isn't on this site any more there isn't anything that can be done about it. There is an option when you click on the group to leave it so I don't know if there is a problem other if it is where you have asked to join a group and it is still pending where you can't remove this from your list so I don't know if this what you are on about.
Thanks its in fact both some where the mod hasnt approved the request usually I see it is they havent been in themselves and some are where I have left the group but the group name still shows in the list of groups I am a member of
I have submitted a Bug ticket but thus far not even responded to
If you leave a group but have friends that are still part of the group and they post in the group discussions, that will show up in your Feed.
I've left a few groups and not had this problem but it might be that the groups I've left were so inactive that there had been no one posting in over a year.
If you're still interested in being a part of any group and the Moderator hasn't logged onto the site in a few months, you can always contact TT2 and request that you be made the Mod and take over the group.
This sounds complicated.
If you are already a group member you can use the Leave the group button which should pop up when you click on the group. (Sometimes you have to go via the Join group button which is confusing). You then have to confirm that you want to leave.
You will be stuck in a hole if you ask to join a private group and it hasn't been approved. It will be stuck on your groups list.
And, yes you will get notice of activity in groups of which you are not a member when your friends do something. You can even respond even though you aren't a member.
BTW I have asked TT2 if I can become a moderator/admin for a group in which the mod/admin hasn't logged into TN for months. She refused.