Can you include a screenshot of the error message here?
The eclipse server view generally only knows about servers it started. IF the server was started outside of eclipse, or somehow survived an eclipse restart, the IDE won't have a reference to the old pid / process id, so it can't communicate to it. It also won't be able to start a new one, since a process is already using those ports. And obviously since the 'server adapter' is marked as stopped, it can't terminate the existing process, again because it doesn't have a reference to teh process id.
I'm one step further. I discovered there was a rogue Wildfly process running, inaccessible from the Ubuntu service interface. This was fixed by a reboot.
Now, I can start/stop a Wildfly server from the Eclipse Servers tab. So far, so good. Now I configured the server as having its life cycle externally managed. While the server status can be accessed from its 8080 port, the server status in eclipse is not correct. Also, a context menu suggests I can still stop the server from Eclipse, which makes no sense. Is this still under construction?
Is there any detailed documentation available on eclipse-wildfly communication? Contrary to your suggestion, process id's don't seem to play a role here, as these are not relevant for controlling Ubuntu services.