My understanding is that brain is composed of way more neurons than required, for resiliency. So if it gets a "bruise" in some part, when even a large portion of the cells are dead -- it can still function at 100%. Like a programmer without a finger. The problem is visible only when all the cells in some part are dead.
That's why crows, with their low brain mass are pretty clever (and why all arguments equating brain size and smartness are wrong).
Just my layman understanding.
Crows (and certain other bird species) have a peculiar forebrain (different in structure but similar in function/evolution to the neocortex in mammals) with neuron counts rivalling primates. So the nr of neurons still matters, but likely not across the entire brain.
my understanding is that extream migrators actualy consume (use as energy) parts of there own brains durring there epic flights, and other species do something similar in the winter and regrow parts of there brains every spring.
It is true that they can shrink some organs to reduce weight and store extra fat, but the brain is not one of them. Would be pretty bad, because brain cells can't regrow like e.g. a liver can.