The supervisor can clear the stuck and closed chats from the profile.
Navigate to the Clear chat tab from the profile pop-up and the following window will be displayed:
Click on 
to clear the monitoring chats of the agents which are closed. Make sure My chats toggle on the header of the supervisor console is turned off, only then all the monitoring chats will be cleared.
Likewise, Click on 
to clear all the incoming chats which are stuck. The supervisor needs to dispose of all the direct incoming chats before clicking on the button.