[quote=Mahz]
Yeah, I was thinking about how that would work since this system is a little smarter than just a dumb inbox/outbox.Perhaps when you "delete" a conversation, your name is crossed off the participants list of that convo. The other participants can resume talking, but you won't receive any sort of notification.
[/quote]

Sounds like a good idea to me. Kind of like Mute for Google+ shares. 

Seems like you'd need a system to regularly delete conversations with no participants (all sides have deleted themselves). Maybe on the last participant deleting?