Services come and go. They serve their purpose or are replaced by a more authoritative source and are deleted. Clients of these services are not notified of this change. We try our best to reach our users but the best possible approach is through the software. Pro projects and web maps will continue to load with a broken service reference but the administrators/users can't tell the difference between a service outage and a thoughtful decision to remove a service.
This is related to https://community.esri.com/t5/arcgis-online-ideas/use-deprecation-flag-through-platform/idi-p/941737 and will fill a missing gap in an often forgotten about life cycle management stage of services.
I propose the creation of a new "shadow" service type or the addition of new service states (currently started and stopped) on existing services to express the intent of the final life cycle stage of a service - deletion. Once the state is set to deprecated, users would be allowed to enter some sort of rich text to explain the situation, link to related issues or articles to help the customer repair their service. This would be served out in the services metadata so the rest of the arcgis platform has the able to react to this data and display it in Pro, web maps, etc.
ArcGIS Server logs would not fill up with clutter about services not being found when they were removed on purpose. It would be great to have analytics on how many clients are still trying to use the deprecated service.