Some extra context for the curious: https://pdf.stafforini.com/parfit-1995-unimportance-identity.pdf
The same goes for people who think they'll be able to upload themselves to a computer. The so-called "singularity". One's consciousness could be lost in the transfer, and no one could tell. You become unconscious and never wake up, you die. The other thing--whatever it is--takes your place in the world, and everyone else treats it as you, but you died. Behind the eyes of that thing, no one is home.