When do Brain Cells Grow Back: A Conjecture

It used to be thought that neurons could not reproduce--that once a given neuron died, it would never replaced. This has turned to be false. Neurons sometimes reproduce. But sometimes they don't. Question: When do they reproduce? My guess is that, when a neuron dies that is part of an otherwise undamaged brain-structure, then that neuron will be replaced; but when an entire brain-structure is destroyed or severely damaged, that structure will not be replaced and, consequently, the neurons that composed it also won't be replaced.