Normally chat will never end when compared to calls. Chat is an ongoing thing. However, it's possible to leave a chat, in which case there are notifications:
Notifications to the person who left chat:
<- CHAT <chat id> MEMBERS username1 username2
<- CHAT <chat id> ACTIVEMEMBERS username1 username2
<- CHAT <chat id> MYSTATUS UNSUBSCRIBED
<- CHAT <chat id> STATUS UNSUBSCRIBED
Notifications to the other people:
<- CHAT <chat id> MEMBERS username1 username2
<- CHAT <chat id> ACTIVEMEMBERS username1 username2
Currently there is not notification when a chat window is closed, but there's a feature request in Jira for that, feel free to add your comments of Vote for it -
https://developer.skype.com/jira/browse/SPA-94Regards,
Mirje