How I imagine what you're thinking of is a kind of small update to an existing model by doing backpropagation training on 'new' data. There are existing proble

How I imagine what you're thinking of is a kind of small update to an existing model by doing backpropagation training on 'new' data. There are existing problems with that, one keyword to lookup is 'catastrophic forgetting', where you update on recent stuff so much that you overfit on that and forget all the prior stuff you learned before. There are methods to mitigate that, but I would call that an 'active area of research'.