I think I understand what you're getting at - that network architectures have a fixed size output - but you're incorrect in saying that the final layer must be

I think I understand what you're getting at - that network architectures have a fixed size output - but you're incorrect in saying that the final layer must be a classifier. In general, you can optimize any differentiable function with gradient descent, and the output does not have to be a probability distribution. The original poster's question does make sense; he's asking what would happen if you trained the network on something like the ILSVRC dataset.