Currently there is an option to "Leave" a 1:1 conversation. This wording is not entirely accurate.
If Person A decides to "Leave" the conversation, the conversation goes to Archive, but Person B is not notified that Person A left and the message. Person B can continue the same conversation and the message repopulates in Person A's Home page and starts off where it left off.
This "Leave" action merely "snoozes" the conversation and does not truly allow the person to Leave.
To make the wording more accurate, would recommend that the word "Leave" be changed to "Snooze" or "Dismiss".