Performance of a damaged brain
To the question "what is happening exactly when brain centres get damaged?". The answer is: When any tissue, including neural tissue, in the body gets damaged, the body will try to repair them. The process of reparation involves many distinct processes, such as the process to get rid of the damaged tissue and the process to regenerate new tissue. But compared with other tissues, such as skin, mucosa, and connective tissue in general, neural tissue has a much more limited capability to regenerate, yet it is not zero. Also, in the nervous system, neural plasticity, which is the adaptation of other neural tissue to perform the function that is impaired or lost, plays the role in the process of reparation too. The following articles may help explain this matter in more details: ref1 and ref 2,  and ref3. And some animal studies of neural plasticity: ref4 and ref5.