I have encountered this bug frequently during multiplayer where one or multiple player character(s) would be flagged as if in dialogue though no dialogue was taking place. Exiting and restarting the game has corrected it in our experience. Visiting camp and resting / ending the day also seems to reset the hanging dialogue flag on the affected character thus allowing saves to happen as normal again. That said, if you aren't paying attention and looking for it, you could potentially lose a lot of progress as the bug seems to disable all forms of saving (normal, quicksave, autosave).
In my multiplayer sessions (myself as the host) we noticed that the hanging dialogue issue was occurring on the joining player characters. We noticed drastically reduced frequency of the issue if the host (in this case myself) initiated all dialogue with NPCs and the other players did not join in to watch the conversation. Initiating or participating in dialogue with NPC vendors/traders (i.e. to buy/sell things) did not seem to produce the issue for either the host or joining players.