This wouldn't be so much for groups, but rather for specific individuals.
For example, I have a user that certain individuals give a hard time. Rather than keep having issues with them, this one user would like to exclude them from being able to reply to his threads.
Sort of like an "Ignore this User" option, but apply it to your threads. Something like "Exclude This User from My Threads."
I like the idea. Kind of frees up mods from dealing with nonsense and cleaning up threads.