Some thoughts I've had on these details and a few points I think are worth mentioning:
First: we have to be careful about comparing mental/physical states like sleep or even deep comatose unconsciousness with notions of mind/body replacement and revival of consciousness. I say this because it's possible that extremely subtle processes might be at work in the former two states that do indeed give us a continuity of perception of same self which wouldn't be the case if you perfectly copied someone and then destroyed them in the instant of reanimating the new perfect copy.
second: for the above i'm not even really taking into consideration the possibility of consciousness being a a partly quantum phenomenon that's impossible to emulate, clone or copy in any way that really recreates the original person's self into a new substrate
Third: assuming we can actually perform whole mind emulation, cloning of a new body and transfer of a self into a new physical or digital substrate (that the brain is capable of being perfectly recreated as if it truly were the original in terms of all functional, practical measurements and subject perception), this still has to keep in mind the danger of what I call uncopied tail end consciousness in the original. In other words, if a person's original self even for a split second or two perceives consciousness beyond the moment of emulation, then truly, they will die and with a knowledge of the copy being just a copy, separate from them, But if on the other hand the transition of consciousness can be made totally seamless as far as perception is concerned, or graduated to that the two gently merge into a new copy, then it would really possibly be possible to create a continuous, clean perception of self.
Fourth, as a tangent of Third. One idea I've always had is of conscious perception having a granular quality, in that we can perceive increments of self awareness/time down to some fraction of a second, and any emulation process would have to create a "backup" for emulation to a new copy at a rate just slightly faster than that natural granularity of perception in order to give us seamless continuity of self-perception in case the original has to suddenly be destroyed and the new copy of your consciousness reanimated.
First: we have to be careful about comparing mental/physical states like sleep or even deep comatose unconsciousness with notions of mind/body replacement and revival of consciousness. I say this because it's possible that extremely subtle processes might be at work in the former two states that do indeed give us a continuity of perception of same self which wouldn't be the case if you perfectly copied someone and then destroyed them in the instant of reanimating the new perfect copy.
second: for the above i'm not even really taking into consideration the possibility of consciousness being a a partly quantum phenomenon that's impossible to emulate, clone or copy in any way that really recreates the original person's self into a new substrate
Third: assuming we can actually perform whole mind emulation, cloning of a new body and transfer of a self into a new physical or digital substrate (that the brain is capable of being perfectly recreated as if it truly were the original in terms of all functional, practical measurements and subject perception), this still has to keep in mind the danger of what I call uncopied tail end consciousness in the original. In other words, if a person's original self even for a split second or two perceives consciousness beyond the moment of emulation, then truly, they will die and with a knowledge of the copy being just a copy, separate from them, But if on the other hand the transition of consciousness can be made totally seamless as far as perception is concerned, or graduated to that the two gently merge into a new copy, then it would really possibly be possible to create a continuous, clean perception of self.
Fourth, as a tangent of Third. One idea I've always had is of conscious perception having a granular quality, in that we can perceive increments of self awareness/time down to some fraction of a second, and any emulation process would have to create a "backup" for emulation to a new copy at a rate just slightly faster than that natural granularity of perception in order to give us seamless continuity of self-perception in case the original has to suddenly be destroyed and the new copy of your consciousness reanimated.