Somebody removed your brain, destroyed it, and then replaced it with another which was identical (and replaced all the connections as they were). Essentially every atom/molecule would be replaced by another of exactly the same type in exactly the same place.
In this situation, it seems reasonable to assume, if we assume that one's experience/consciousness is a product of their brain, that from your perception, you simply die. Your brain is removed and destroyed: whatever happens after that does not matter. It's just that there will now be a person who thinks they are you and that they have always been you (the new brain), but they are mistaken.
Your brain is replaced molecule by molecule, atom by atom, in a way that does not interfere with the working of the brain (each bit is replaced by an identical bit only at a time when that bit is not being used and so the process happening in the brain is not disrupted).
Is seems reasonable in this case to assume that from your perception, you do not die. (If this is not the case then would that mean you would die slowly, in proportion to how much of your brain has been replaced? How would your consciousness fade out if the process in your brain is not being affected?)
In scenario 1, the process is completely stopped and replaced by another idential process. In scenario 2, the process is not disrupted. This implies that consciousness is the process (or multiple processes?) happening inside the brain.
Therefore, does this imply that cases where people die momentarily (ie are brain dead and then reawaken), from that persons perspective they just die. And when "they" reawaken it seems to everybody else that they are back, but actually they have just been replaced with another completely identical person?