I looked at the service manual, available on my server if you click the link in my signature area below, and its called a sprocket cover in the service manual. The best i can tell is its there solely to protect the sprocket, it would also probably catch the chain when it broke but thats besides the point.
I doubt thats why the chain broke, and the last person in there probably just forgot to put it back on. I don't see any reason it would hurt to run without it, but i would suggest you get it replaced. Someone has to have one used! I would post up in the classified.
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1984 Honda ATC200ES "Big Red"
1982 ATC200E "Hondie"
1988 TRX300FW "Project Quad" Still in progress....