When operator goes offline, set up to close chats automatically, so clients aren’t left unanswered. When client receives a new message, another operator can accept this chat. In the section Settings-General choose the function «close open chats of operator, supervisor or admin when they log out or become inactive».
You can warn operators about incompleted chats, when they logging out or changing status from “online”. Also can set up it in the section Settings-General-Warn when logging out or changing status from online. Here write the text of the message, which operator will see when try to change status.