After importing our vB data into XF, we had a ton of outdated and forgotten PMs that were converted into XF Conversations.
I had no idea there was no (XF core) provision to remove those old discussions and was even more surprised when I learned an Admin could not mass-delete them.
After a brief bit of snooping around, I found AndyB's Conversations Prune add-on and with just a couple of setup parameters it was off & running. Even better yet once you set it, you can forget it as it'll continue to tidy things up for you in the background. The suggested Phrase Edit is an excellent idea, in order to let your users know just how long older conversations will stick around before being removed.