In modern NN's, it's a real pain adding new classes on the fly, and if they're not known at the outset, it typically requires retraining the network (either fully or just a handful of layers).
However, let's say the task was to classify species. The network is trained on 20 animals, and up until this point, has no knowledge of a Horse.
If you were to describe a Horse, you might say it was some combination of Cow, Zebra etc. Similarly, if you showed the trained network 100 images of Horses to infer the class, has anyone demonstrated accurately being able to represent a new class as a composite of existing classes? It could predict a Horse as a composite of a cat and a fish, as long as it's consistent, that information is useful.
I.E if for the vast majority of those images you saw a prediction similar to: 0.7 Zebra, 0.2 Cow, 0.1 Dog. I understand the layers in your standard CNN are unlikely to highly correlate a Zebra and a Horse in the same way Humans do, but that's not really an issue. As long as it's prediction for that new unknown class is consistent across those new images, if you had a handful of unknown classes, you could cluster them separately from each other.
I've looked around for papers to see if this has been assessed but struggled to find anything relevant.