Screw-in eyepieces can loosen, unscrew, and fall out, often unnoticed until later. Some owners put glue of some sort on the threads and screw the eyepiece in to prevent it from unscrewing. If a permanent adhesive, such as epoxy, is used, removing the eyepiece can be difficult or impossible.
The Nikon eyepiece show in the link in post #1 has a rubber ring bonded to the eyepiece. This isn’t meant to be separated from the metal part.
As described in post #1, it might be that the rubber part is loose on the eyepiece. If so, possibly the rubber ring is turning independently 1/4 turn, but the metal ring beneath is firmly stuck in the camera without rotating.
I’ve encountered this problem on used Nikon cameras and used a Flexiclamp similar to the one shown in the following link. The tool should be chosen with a hole size slightly larger than the ring you want to remove. The part might have to be wrapped with one or more layers of masking tape to take up the excess clearance so that the tool will have a strong grip on the part when the handle is gripped to contract the hole in the Flexiclamp.
Dead Link Removed
Based on the photo in post #3 of the Nikon N8008 eyepiece area (appears to be recessed), there might not be sufficient clearance to use the Flexiclamp to grip the eyepiece.