For any of this to make sense, we’re going to have to describe some basic assumptions about the nature of reality, consciousness, and how the two interact. Reality will be assumed to follow that which is described in the Many Worlds Interpretation of Quantum Mechanics (MWI), or at least one interpretation of that description. Here this means that all outcomes of a probabilistic system exist in a superposition, that is to say that for every outcome of a situation there exists a branching world wherein this is the outcome realized. For the purposes of this discussion we will be talking about large, discrete steps in time and very limited numbers of outcomes. Consciousness will be assumed to be inherent in your existence and to span across these branching worlds as an observer of each world. Observation will be the way in which we will define the branching of worlds, such that worlds only exist if they can be observed by a consciousness.
One idea that I will leave unclear so as to leave room for further discussion is the extent to which biology can dictate conscious observation. Observation can be split by biology into sensation and perception; typically we only consciously observe perception, but perception only exists as the filtration and augmentation sensation. The brain must receive signals to process in order to create a perception, but these do not necessarily exist to the conscious mind and so can be argued to not be observed. Nonetheless, these signals dictate the perception that is created and so can be said to be the base layer of which perception is an abstraction. However, some interaction will need to be clearly defined, specifically the idea of memory. While there is plenty to debate in regards to whether an experience is truly valid if there is no memory of it that can be accessed by the consciousness, in this case we will be assuming that any experience which cannot be remembered will not exist in the reality defined by said consciousness. It should also be made clear, for completeness, that memory is stored in the brain, a physical entity that may exist in superposition across multiple worlds but which can only act in a given world as a being in a singular state.
A context is necessary to fully discuss the concept of death within, so a system of timelines and superpositions will be defined. Any given state that can be observed by a consciousness (i.e. a world) will be denoted $\Psi_{\psi_1,\psi_2,\psi_3…}$, where $\psi_n$ is an index of the outcome of the probabilistic decision $n$. This would mean that after some initial decision our universe’s state will be a superposition of $\Psi_1$, $\Psi_2$, $\Psi_3$, etc. After the next decision along the timeline defined by $\Psi_1$, $\Psi_1$ will become a superposition of $\Psi_{1,1}$, $\Psi_{1,2}$, $\Psi_{1,3}$, etc. This essentially defines an n-dimensional matrix of states derived from a singular origin point which we will refer to as $\Psi_0$. As previously mentioned, consciousness spans parallel/simultaneous worlds, we will define each discrete step in time as the creation of a new decision such that all states which are denoted with a given number of subscripts will exist simultaneously. Since $\Psi_0$ evolves into the superposition of states $\Psi_{\psi_1}$ for all values of $\psi_1$ and the conscious observer after the first discrete step in time spans all states $\Psi_{\psi_1}$, it can be said that this consciousness encompasses all that is yielded from $\Psi_0$ when time acts upon it. Furthermore, any state $\Psi_{\psi_1}$ will evolve into a superposition of all states $\Psi_{\psi_1,\psi_2}$ after the second step in time (for convenience we can refer to this as $t=2$), at which point the conscious observer will span all that is yielded from any state $\Psi_{\psi_1}$ when time acts upon it. These ideas combined suggest that consciousness defined in this matter will experience all possible outcomes propagated from $\Psi_0$; this can be considered a deterministic system.
What it means to experience, or observe an experience, must also be discussed. This is essentially the question of “if a tree falls in the woods and nobody is around to hear it, did it fall?” Given that we have defined a world as that which is observed by the consciousness, the answer to this is simple: no. Any event that has no means by which to be observed by our observer does not exist. It may be beneficial to view the “observer” as the portion of the consciousness that is present in the timeline being observed here. This idea must also be expanded into the concept of remembering experiences. If an experience cannot be remembered, did it happen? Of course, in this instance, we’re viewing memory as a true record of happenings, which is not necessarily true. However, if an event cannot be remembered, it may still have left an impact on reality that would encode information about the event having happened that can be retrieved by some means which we will for the time being consider remembering said event. So if even with this loose definition of remembrance an event cannot be remembered, it can be said to not have happened at all.
Finally, we can discuss the effects of death in this system. Let us take the observer in the state $\Psi_{1,1}$ as an example. This observer is nothing more than a single state in the superposition with all other states $\Psi_{\psi_1,\psi_2}$ as per our definitions, but is still functionally a person that is experiencing life. If this observer dies as it reaches the third decision ($\Psi_{1,1,\psi_3}$), then what effect does this have on the consciousness of which this observer is a state? All states at $t=3$ are still states of the consciousness, but in some states (let’s simplify this down just to the individual state $\Psi_{1,1,1}$) there is no longer an observer allowing the consciousness to experience the associated timeline. As such, the world in $\Psi_{1,1,1}$ and subsequently all worlds stemming from it when $t\gt3$ ($\Psi_{1,1,1,\psi_4,\psi_5,…}$) cease to exist. Consciousness continues to exit, however, spanning the superposition of states $\Psi_{1,1,\psi_3\neq1}$ (assuming that no other observers have died). This process will occur at any decision wherein an observer dies, until there is no longer any available observers of the consciousness, at which point the universe as defined by the consciousness ceases to exist as a whole.
Lived experience is less simple to describe since we do not have a thorough understanding of how the consciousness is linked to these observers. It is possible that the experience of one observer continues on, becoming an observer that has not died. In the previous example, this would mean that the observer that would have experience the state $\Psi_{1,1,1}$ would instead experience some state $\Psi_{1,1,\psi_3\neq1}$, in this example we will assume this to be state $\Psi_{1,1,2}$. Since experience requires continuous access to memory (as previously discussed one cannot experience that which one cannot remember) this observer would not experience its own death but continue living as if it were the observer in the timeline of $\Psi_{1,1,2,\psi_4}$ since $t=3$. That is to say that the observers within the consciousness will never experience their own death, continuing to shift from timeline to timeline to avoid doing so until the consciousness itself ceases to exist.
Who are you, then? Are you the consciousness? Are you a single observer? We tend to describe ourselves as our minds and bodies, something that physically exists, something that can die. But if the previous ideas are correct, then your consciousness will not always be in that mind and body that we consider you to be, it may never experience the death of that body.