I believe that what defines a person is a pattern of neurons firing in the brain. I also believe that if said pattern could be perfectly replicated on some other medium (along with all the associated physiological inputs that keep it humming and changing), that new pattern would be indistinguishable from the original.
There are infinite possible outcomes to every action, branching off from each moment. And there are also infinite parallel realities that branched off of previous moments. The pattern that is your consciousness will also branch off infinitely. But imagine a fork in the road where one direction is death. Your consciousness cannot take that route, because it no longer exists on that branch. But it DOES still exist in the other, and it has no choice but to continue onward.
Thus, you will never experience death.
Your consciousness may change along its beaching paths, perhaps contorting into something completely new, but it will never truly end.
This conversation reminds me of the book, Fall, by Neil Stephenson. In it, the main character dies but his essence is captured in software. It raises a ton of interesting questions about that process, including how would a software version of the brain function without the other organs, blood flowing through it, etc. In my head canon, it couldn't. I.e., we are the sum of all of our parts.
Well the thing is, it would change without those inputs. It would have to adapt to new inputs.
One would imagine that any successful replication of a human mind in technological form would also need to replicate those inputs - at least at first, until the pure mind itself could be weaned off them - if that's even possible. They are, after all, just another series of electrical signals, but they are also integral to a sense of self.