Lightning strikes me and I die. Fortunately (let's suppose), the universe is infinite and consciousness supervenes on the arrangement of molecules in one's body. So somewhere in my forward light cone -- maybe in about a double-boggle years [note 1], arises an enduring, Earthly, Boltzmann continuant of me.
A Boltzmann continuant for Person X at time T is, I stipulate, any being that, at time T-prime, arises suddenly from disorganized chaos, into a entity particle-for-particle identical to Person X at time T, within an error range of a thousandth of a Planck length. [note 2] A Boltzmann continuant is enduring just in case it survives in human-like form for at least one day. A Boltzmann continuant is Earthly just in case it exists in an environment that, at time T-prime, is particle-for-particle similar to Earth at T, within a range of 10,000 light years, and obeys the same laws of nature -- except allowing for minor differences in features that had not been observed before time T but would be plausible epistemic possibilities to human observers, such as the unobserved top of a cloud twisting one way rather than another, an unobserved flower in the Sierra being one centimeter to the left, differences in the details of how storms play out on distant planets, etc.
According to mainstream physics (back to Ludwig Boltzmann), there is an extremely tiny but finite chance that such an enduring, Earthly, Boltzmann continuant of me could arise. So if the universe exists long enough and doesn't settle into some inescapable loop, presumably I will eventually have a Boltzmann continuant.
By hypothesis, my Boltzmann continuant is not killed by the lightning strike; he survives at least one day. Maybe he survives a near miss with lightning. By hypothesis, my Boltzmann continuant will have the same arrangement of molecules in his body at time T-prime as I do at time T; and since the environment is Earthly, presumably things will proceed fairly normally from time T-prime forward, despite the chaos before time T-prime. By hypothesis, consciousness supervenes on the arrangement of molecules, so presumably my Boltzmann continuant will have conscious experiences very much like the ones I would have had if I had not been struck by the lightning. Maybe my continuant will have an episode of thinking to himself something like "Wow, that lightning struck close! I'd better get inside!" [note 3]
Earth is a pretty safe and stable place. So too, then, is continuant-Earth. My continuant returns "home", greets the continuant versions of his family, comes to the continuant version of his office, works on a post for the continuant version of The Splintered Mind. I have no future. He has no past. But we hook together seamlessly into one "Eric Schwitzgebel" with an undetectable double-boggle-year gap between us. Call the entity or quasi-entity composed of these two parts gappy-Eric.
In a way, it would be odd to think it mattered hugely that there is such a gap between these two half-Eric Schwitzgebels. From the inside, gappy-Eric will feel just like he's a continuous, Earthly Eric Schwitzgebel. From the outside, too, at least through the next 10,000 years, no one on continuant-Earth will have cause to suspect a gap in Eric or in the world. Gappy-Eric's family life, his professional life, the whole planet -- all would seem the same, all would seem to continue unabated. Continuant-existence would seem to be survival enough.
Of course, I needn't be struck by lightning for there to be enduring, Earthly, Boltzmann continuants of me. If we accept the that the universe is infinite, diverse, and subject to Boltzmannian chances, then every time slice of me will have an infinite number of enduring, Earthly, Boltzmann continuants somewhere in the future. So I needn't fear any early, chancy death: Some appropriate Boltzmann continuant of me will launch at precisely the right subjective moment to continue me seamlessly. Gappy-Eric lives! In some cases, going back a few seconds might be necessary to find an appropriate time T from which my death was not inevitable in any Earthly environment, but it seems like quibbling to think those few seconds make a huge ontological difference.
With infinitely many continuants of me, sprouting off from every moment of my life, whose continuant-bodies on continuant-Earth are for practical purposes as good a continuation of me as is my own body on Earth, maybe I shouldn't care about my individual death at all, in any circumstances -- or rather maybe I should care about it only as the loss of one soldier in an infinite army of me.
Yes, this is entirely bonkers.
[note 1]: The standard view is that there are about 10^80 particles in the visible universe. A googol is 10^100 (or 10^(10^2)), i.e., the number of particles in 10^20 visible universes. A googolplex is vastly bigger: 10^googol! (That is, 10^(10^(10^2))).) But even that isn't big enough. So I define a boggle as 10^(10^(10^(... a googolplex times ... ^10))). A double-boggle is a boggle^(boggle^(boggle(^... a boggle times ... ^boggle))). Now that's big. Maybe big enough.
[note 2]: I assume that differences of less than a thousandth of a Planck length don't matter to consciousness. If necessary, we can narrow the error range. If we use an ontology of fields, presumably an error measure similiar in spirit could be developed. There will also be an issue about temporal spread -- perhaps more serious if consciousness spreads across a specious present. If necessary, there could be a brief period during which consciousness slips into the Boltzmann continuant before full supervenience takes hold.
[note 3]: The question arises whether the continuant's thoughts would have that meaning, if the meaning of words depends on facts about learning history; but given our stipulations, at least the continuant's conscious experience of that episode of inner speech will be like mine would have been, even if it doesn't tack down its reference in the external world in quite the right way.