I plan on being non-existent soon, but don’t worry, I plan on coming back into existence shortly afterwards. You see I do this thing called sleep on a regular basis, which is often dreamless sleep. (Well, they say that everyone dreams, but that not everyone remembers their dreams, which raises some interesting questions about what it means for an experience to be conscious and its connection with memory, but that is a subject I have already discussed. In any case during the night there will be some periods without dreams.) Now during this dreamless sleep my consciousness will not exist; consciousness is a process, a type of activity, and that activity simply isn’t occurring in a dreamless sleep (or at least this is the most likely possibility). And so since I identify myself with my consciousness, and not with my body, it makes sense to say that during the night I will not exist.
Now some will say that my consciousness does still exist, even during a dreamless sleep, because even in sleep the potential still exists in my brain to continue the process that is my consciousness. But to assert that this is enough to say that my consciousness exists during that time is to say that my consciousness has always existed and will always exist, and exists everywhere. This is because everything has the potential to continue my process of consciousness; it’s just that some things need to be changed more than others to do so. To go from sleep to my waking consciousness is only a small change in my brain. But someone else’s brain could also begin a process that would count as my waking consciousness, with enough changes. And with even more alterations even a rock or a bucket of water could continue the process. So, while it is not inconsistent to claim that the potential allows us to say that my consciousness still exists, I think it is ill-advised to do so, since it would make the existence of my consciousness trivial.
Now the possibility for other objects to continue my consciousness is an interesting one. Admittedly such an occurrence would never happen within our lifetimes, or even the lifetime of the planet. However, because of quantum background fluctuations, there is a non-zero probability that some matter will come into existence at any given time (a very low probability though). And thus there is an even lower probability that an arrangement of matter that continues your consciousness will come into existence. In fact this probability is so low that one would have to expect an unbelievably long period of time to pass before it would occur, a time vastly longer than the current age of the universe. But if the universe doesn’t come to an end then we should expect it to happen eventually, assuming that the quantum fluctuations don’t “die down” (become more unlikely in the older universe), which they might. But I wouldn’t be looking forward to this possibility as some kind of substitute afterlife; such continuations of your consciousness would likely be brief, and the experiences had would be basically random. And they are equally likely to continue any part of your life. Given that I think we should be hoping that such continuations don’t occur.
But anyways, back to my main topic, which is that everyone “experiences” non-existence on a regular basis. Or rather I should say that they have enough information to know what non-existence is like. Specifically that it isn’t like anything, and certainly not something unpleasant. Of course people still fear it, but I think the best analogy to that fear is having a bank account with an unknown amount of money in it. You might worry about running out of money, but such worries aren’t really justified, it makes more sense simply to enjoy the money that you do have instead of constantly wanting more, given that you didn’t do anything to earn the money in the first place, and that there is little you can do to deposit more.