The problem is when a user sign out of the site (the signout call ChatSystem.Stop()), but the Messenger window remain open, then some errors appears because like you say the ChatSystem has been stopped, the idea is handle all those errors and the options I thought are:

a)      Catch the errors that appear in the messenger and in his place give to the user one custom message and ask him to close the messenger window.

b)      Catch the change in the status of ChatSystem in the messenger page and close the messenger page.