If a service is stopped using the ArcGIS Server Manager, the service's Portal item page still exists but gives no indication that the service has been stopped. If you attempt to open the service in the map viewer, it returns a generic error ("unable to add layer"). It would be very helpful if the Portal item page and map could indicate the service is stopped and allow the admin to provide a short explanation and/or contact info.
Alternative/additional option: The admin should have the option to hide the portal item when stopping the service. I'm surely not the only one who stops services indefinitely before deleting them. Like putting a file in the Recycle Bin before emptying or restoring it.