You can't directly close their database, but you can, with a timer event and
a one record, one field table in the back end, cause theirs to close.

It does require either a form that says open as long as the app is running,
or a timer event it every form.  (The first is better and has some other
benefits)

Set the form's timer event to check the value of the field and take the
appropriate action, for example:

   If blnTimeExpired Then
       Docmd.Quit
   End If