Your conversational partners are substantially more polite than mine :) It's not even remotely uncommon for people in my circle to leave an IM or even a group

Your conversational partners are substantially more polite than mine :) It's not even remotely uncommon for people in my circle to leave an IM or even a group chat in the middle. We all have dozens of things going on at any given time and it's expected that, unless the conversation is Really Important it will take second fiddle to the emergency of the moment. So for us all conversations implicitly fit into your second category unless pretty explicitly stated already. I concede, however, that if your typical behavior doesn't fit this model already wave is likely to be somewhere between useless and actively frustrating.