A Shutdown Items folder existed on the Macintosh as of System 7.5. It was a somewhat belated response to the existance of the Startup Items folder.
As the name suggests, any items in this folder would be launched by the Mac automatically upon system shutdown. (This would only be the case, though, if the system underwent a normal shutdown procedure.)
A "farewell sound" or a copy of a backup utility could be placed, to make use of the Shutdown Items folder.