If you mean you're seeing cases where you can right-click on the notification area icon for the VisualCron Tray Client and mouse over the Server item and it shows "Server Off" and the option to "Start" is enabled, but if you open the main client the server is actually On, then I'm not sure what options you really have; that sounds like a bug.
If you mean the notification area icon for the VisualCron Tray Client is red, and when you right-click and mouse over the Server item it shows that it is not connected to the server - which I get a lot, but isn't really important in my deployment case - then I think you would need to submit a feature request, as there is a VisualCron event trigger for User Logon, but there isn't one for User Logoff. The trigger would also need either to provide a variable exposing what user caused it to fire or to allow specifying what user(s) should trigger it. What you would need, as far as I can tell, would be a job that triggeres on User Logoff and sends a notification if the user that logged off is the built-in VisualCron Tray Client User.
Another possibility that wouldn't require a new feature, but which is rather a lot of effort, would be to write a job with a task that interrogates the VisualCron API (either the REST API or the .Net API) to see whether the VisualCron Tray Client user is currently connected (and possibly from what addresses, if you have the tray client installed on multiple machines) and sends a notification if that result is not what's expected. I don't have an example for that handy because it isn't something I've ever needed.
I'm pretty sure based on your topic description that what you're looking for is not a notification when the server status actually changes from on to off, nor if the service actually stops, but just in case: There are VisualCron event triggers for both of those, and I do have a job that triggers on those events and sends a notification (among other things); however, while that seems adequately reliable for the Server Off event, it won't reliably trigger for the Service crashing and I'm not sure it will reliably send the notification for the service stopping (especially if it's stopping due to the host shutting down), so if you do need to monitor for the service stopping you may need to use another facility for that