What would cause an "automatic" adding and removing of members of an iMessage chat?

There are 4 members in this iMessage chat (all family members). After almost every message, I see the notification that member A is adding member B to the conversation by Member B's icloud.com account and removing Member B from the conversation by his phone number.

Later, I'll see the notification that Member B is adding himself to the conversation via his phone number and then removing himself from the conversation via his icloud.com account.

Neither member is doing this. It is just showing up as having been done.

Has anyone seen this type of thing before?