Tell him to close the last drawing first.
Seriously though, for something that strange I would try running a repair first, and if that doesn't work do a clean uninstall & reinstall.
Welcome to the forum.
Does he just have drawings open or does e have the corresponding models open as well?
What I would suggest is only open a couple if not one at a time combination model and drawing.
Also, have they tried these files on other machines?
Another thought is have there been crashes other then 2012 just not closing?
I am wondering if there are temporary files stuck in the working folder that are from crashes
that are screwing this up. I would check the working folder and clean out the working files (the ones with
the $ infront of them).
I will throw this out there as well. You might after all of this before you do an uninstall and reinstall
running the Solidworks Rx tool and see if that shows anything.
I am having this same problem. With a drawing file open, all Close and Exit options are greyed out, I can open and close other files (i.e. the part files) but the close options for the drawing file/window are not available. Clicking the close (windows) icon doesn't do anything either.