Thank you for taking the time to reply @Emi Zhang-MSFT
Did only Word have this problem?
-Only Word is having the problem. All other Office apps exit without issue.
Did this problem appear in all Word documents?
-So far it's happening in every document we've tried.
If this problem only appear in specific document, where did you save it?
-The documents we are working with are on the desktop.
Try to test if you can close Word by Alt+F4.
-I have not tried this yet, but I will.
Remove the file named: Normal.dotm (Or you can cut to Desktop), then restart Word.
-I forgot to mention that I tried this previously, but it didn't change the behavior.
You can also run the Antivirus software to check if the computer is attacked.
-Antivirus (Sophos) hasn't reported any issues on this computer.
Or try to disable firewall and antivirus software, maybe they disable any options or shortcut key.
-I have not tried this, though since closing the document works after we've "enabled editing" then closed (via taskbar) and opened again, I suspect this will not help.
Thanks,
Jesse