Would one be viewing these conversations or just knowing that one has been started?
Viewing is a dangerous road...however, as an added thought, viewing a MemberCard (as admin) and knowing they HAVE conversations would be super helpful (versus needing to access the ACP to see their conversation count) MemberCard currently shows Messages, Media, Reactions, Badges, Points (well, mine does)....easily knowing a "no post" member has active Conversations would be a first step.
Or a trigger that notes: Usergroup X (ie: 5 or less posts) and conversations greater than 0.
Knowing would be a good start....fancy would add keyword triggers ...ie: phone prefixes, email domains, words like Venmo or gmail to the trigger list. (for whatever reason, Cedar Rapids IA is a hotspot for scammers right now....well, unless you count their Nigerian IP addy....lol) (oh, and scammers who have Paypal issues, but their girlfriends Venmo works fine)
My IP and other triggers are working decent...for now....
Side comedy: Had one scammer (has about 30 blocks thus far) actually used the Contact Us twice in 10 minutes from two different usernames to complain they had been blocked as Spam....from a Nigerian IP....at the end of the day, I hope I'm smarter than they are
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edit: Call it a "conversation monitor"