Do any events fire when the Flash Player exits?

Question

Hey all.
I use a LocalConnection object to prevent being able to run our SWF multiple times on the same computer.
The problem is that this connection can remain in place even when the SWF which called it closes. 
I have:
1) An External Interface call to dispose() all HTML pages call dispose() on pageunload which closes the connection.... But this is unreliable because if the browser crashes, you are locked out of the SWF
2) I tried some crazy try/catch.  If SWF A exists and SWF B tries to be initialised.... SWFB cannot connect so it sends a function to SWFA to dispose(). This should free the connection for SWFB to connect to?  But this does not work well either because sometimes a localconnection can be in use but calling "dipose()" throws an error, often because the LocalConnection swf which should be available is already gone.
What this all comes down to, is that I need a way to detect when the player closes, so i can close the localconnection.
stage.addEventListener(Event.EXIT, onExit);
function onExit(e:Event): void
         if (localconnection)
                localconnection.close();
Does anything like this exist?
Thanks,

Answer 1

Thanks for taking the time to answer kglad!
I should have been clearer it is a Web App, so your answer remains valid.
I have not completely followed you on your advice.. When you say "So it only prevents another swf from running if something is returned from a currently running swf".
Could you expand on that? I am desperate to fix the issue, but it just seems localconnection is not the best method for "single swf execution". I just have not found any other methods.
Thanks.