Well, no, of course not- when a neuron dies, the information encoded in it's connections is lost. [1] But replicating the original connections isn't necessary,

Well, no, of course not- when a neuron dies, the information encoded in it's connections is lost. [1] But replicating the original connections isn't necessary, and certainly not necessary for the neuron to "compete." For example, say an old corporation dies, e.g. Microsoft [2]. Could a new corporation replicate the 1000s of precise products, services, and contracts of the original? Not at all. But replacement corporation could find new things to offer, potentially taking advantage of the economic shortfalls and new demands precipitated by the demise of Microsoft. Eventually the economy returns to full efficiency, though in a slightly different form than before. And just so with neurons- the information passed through the neuron that died will now be in demand by neurons downstream, and this demand can be fulfilled by new connections by the new neuron (or new connections from old neurons, or simply not.) But the information may come from different places, or have slightly different semantic value, or other differences. [3] Brains, like economies, change, and are good at changing gracefully. [1] At least, as far as we know- with glial cell participation and functional viral capsids and whatever else is going on, anything is possible, I guess. [2] Example chosen without malice. Honest! [3] All assuming the competition model of neural organization. Which is a plausible model last I checked, but see [1].