Be aware that strictly speaking AutoExit is not run when Word closes, it is
run when that template is unloaded.

If the AutoExit is in normal.dot, normal.dot is only ever unloaded
immediately prior to Word closing so this is a distinction is without much
of a practical difference. But for add-ins, the AutoExit macro will run also
if you go to Tools, Templates and add-ins, and uncheck the template in the
addins list.