Does anyone have any real-world, object-level examples of degenerate cases)?
I think degeneracy has some mileage in terms of explaining certain types of category error, (eg. "atheism is a religion"), but a lot of people just switch off when they start hearing a mathematical example. So far, the only example I've come up with is a platform pass at a train station, which is a degenerate case of a train ticket. It gets you on the platform and lets you travel a certain number of stops (zero) down the train line.
Anyone want to propose any others?
Not going anywhere is degenerate travel (but can be an especially restful vacation).
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.