A lot of people ask us why FogBugz doesn't automatically tell the submitter when a case is closed or resolved. The short answer is that we only allow FogBugz to send email to non-FogBugz users when a FogBugz user explicitly tells it to do so.
FogBugz users are part of the system and have elected to receive email notifications. If these people are FogBugz users, they can create cases directly in the system and use Autosubscribe to subscribe to cases they create.
The one exception to this is the confirmation email that you can choose to have automatically sent to your correspondents to verify that their email was received.
We made this design decision because we found there were too many situations in which an automated email to a user outside FogBugz would only result in more confusion and more work for FogBugz users. If you want to send a form email to your users on closing their issue, you can do so by creating a snippet and sending that to the correspondent.