We may be close to being able to extend human life. Ending death entirely seems a bit less plausible; even a person who doesn't age can still die by accident, and I'm not sure how the probability of any person experiencing such a random accident can ever drop to zero.

My optimistic view is to look at self-awareness as a very surprising thing that doesn't make any sense. As far as we know from biology, I should be basically a biological robot that can use its brain to solve problems but without any real sensation, just reaction to stimuli. If self-awareness isn't an emergent property of complex biological machinery, maybe it isn't entirely dependent on it either. I can't imagine how self-awareness would work without a body or a brain to connect to it as an interface, but perhaps there's more to souls than is apparent and maybe those do last forever in some form.