There will be no future personal state of non-experience to which we can compare our present state of being conscious. All we have, as subjects, is this block of experience. We know, of course, that it is a finite block, but since that's all we have, we cannot experience its finitude. As much as we can know with certainty that this particular collection of memories, desires, intentions, and habits will cease, this cessation will not be a concrete fact for us, but can only be hearsay, so to speak. Hence (and this may start to sound a little fishy) as far as we're concerned as subjects, we're always situated here in the midst of experience.
Even given all this, when we imagine our death being imminent (a minute or two away, let us suppose) it is still difficult not to ask the questions "What will happen to me?" or "What's next?", and then anticipate the onset of nothingness. It is extraordinarily tempting to project ourselves--this locus of awareness--into the future, entering the blackness or emptiness of non-experience. But since we've ruled out nothingness or non-experience as the fate of subjectivity what, then, are plausible answers to such questions? The first one we can dispense with fairly readily. The "me" characterized by personality and memory simply ends. No longer will experience occur in the context of such personality and memory. The second question ("What's next?") is a little trickier, because, unless we suppose that my death is coincident with the end of the entire universe, we can't responsibly answer "nothing." Nothing is precisely what can't happen next. What happens next must be something, and part of that something consists in various sorts of consciousness. In the very ordinary sense that other centers of awareness exist and come into being, experience continues after my death. This is the something (along with many other things) which follows the end of my particular set of experiences.
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As I tried to make clear above, subjectivities--centers of awareness--don't have beginnings and endings for themselves, rather they simply find themselves in the world. From their perspective, it's as if they have always been present, always here; as if the various worlds evoked by consciousness were always "in place." Of course we know that they are not always in place from an objective standpoint, but their own non-being is never an experienced actuality for them. This fact, along with the fact that other subjectivities succeed us after we die, suggests an alternative to the intuition of impending nothingness in the face of death. (Be warned that this suggestion will likely seem obscure until it gets fleshed out using the thought experiment below.) Instead of anticipating nothingness at death, I propose that we should anticipate the subjective sense of always having been present, experienced within a different context, the context provided by those subjectivities which exist or come into being.
In proposing this I don't mean to suggest that there exist some supernatural, death-defying connections between consciousnesses which could somehow preserve elements of memory or personality. This is not at all what I have in mind, since material evidence suggests that everything a person consists of--a living body, awareness, personality, memories, preferences, expectations, etc.--is erased at death. Personal subjective continuity as I defined it above requires that experiences be those of a particular person; hence, this sort of continuity is bounded by death. So when I say that you should look forward, at death, to the "subjective sense of always having been present," I am speaking rather loosely, for it is not you--not this set of personal characteristics--that will experience "being present." Rather, it will be another set of characteristics (in fact, countless sets) with the capacity, perhaps, for completely different sorts of experience. But, despite these (perhaps radical) differences, it will share the qualitatively very same sense of always having been here, and, like you, will never experience its cessation.
