If we have classified 1000 people's faces; how do we ensure the network tells us when it encounters a new person?
You can't really make the network tell you if a face is new (unless you actually train a network with that particular purpose, maybe). Ideally, if you feed a new face to a trained network, the output activations will be pretty low in all the possible categories (faces that the network has already seen) i.e. no particular category will signal a high probability. In that case, you can just set a cut, such that if the maximum activation is below a certain threshold, it means that the NN encountered a new face. But things are not that easy in practice. If the NN encounters a face it has already seen, but the image is weird (blurry, the face doesn't cover much of the actual image, there are multiple faces in the image etc.) you could get the same output as in the case of a new face. At the same time, for a NN images are just probability distributions, so it could happen that a new face, which for us, humans, looks nothing like the others, to look pretty similar to an old one, from the NN point of view, hence giving a high activation in a single particular output neuron.