I assume everyone is familiar with the multiverse theory. How every random quantum event, every decision, every moment, creates a bifurcation in the time-space continuum - one in which the event happened, and one in which it didn't.
It provides an easy solution to problems such as Schroedingers cat. While the box is closed, there's an overlapping quantum state, in which the cat is both alive and dead. But the moment you open it, there'd simply be a bifurcation. In half of all infinitely many universes in which the box was opened at that moment, the cat would be alive, in the other half it would be long dead.
You can already guess how this could lead to immortality. Obviously, as long as there's any chance, no matter how unlikely it is, that the cat might be alive, there would also be some multiverses in which it actually is.
But of course there's also infinitely many in which it isn't. So YOU might as well be in one where it's dead. Another YOU would be in one where its alive, but that doesn't help you. You have no way of resurrecting the cat.
However, this is suddenly different if you are the cat. Because the cat - or rather the cat's consciousness that can perceive time and space - exists ONLY in those universes, where the cat is alive - at least beyond the moment it was killed.
This eliminates every universe that the cat died in from the cat's timeline.
For you, the same is true. By the time you are reading these lines, there has been near infinitely many bifurcations of your existence, but in all of those where you ceased to exist (or never existed in the first place) - you would obviously never read these lines.
This includes very very VERY unlikely chain of events. You can tell that the likelyhood of our universe forming with the right parameters, the unevenness between matter and antimatter, our galaxy being undisturbed by mayor calamity's such as gamma-ray-bursts for long enough, our planet forming around the right type of star in the right distance, which a series of catastrophes that both formed a stabilizing moon and made the conditions for development of life right (late heavy bombardment and such) all the way down to humans and furries evolving and YOU actually being born -- is NOT particularly high.
But since you do exist, you limit the number of infinitely many possibilities down to still infinitely many possibilities where you exist.
This continues to be the case.
In some universes, in 3 seconds you will spontaneously die:
3.
2.
1.
click!
Still here? Well, lucky! You happen to be in a multiverse where you didn't die. Granted, the likelihood of spontaneous death wasn't too great, but it was higher than zero. In some universes you just got snuffed - but - by definition - you are not in these universes at this point in time.
But the same logic can of course be applied to any existentially threatening event. Including those with a relatively high risk of not making it out alive.
What if you are terminally ill, and nothing in the world can save you? Or you just jumped off the cliff into a Volcano (or were thrown) and you see your life flashing in front of your eyes. Will you end?
Well obviously you will end, in the vast majority of multiverses, but in those you will not be able to remember it later. There is no continuity. So the ones that actually matter are the ones where there IS continuity and you somehow get to tell the tale (at least to yourself)
Now the issue here is probabilities. The probability of being saved by a random large scale quantum event and teleporting to a safe space, or against all odds surviving complete physical annihilation is just so low, that it's extremely unlikely for you to end up in that. This wouldn't matter, if that's the only possibility (cause then the universe would force you to that solution) but there are other, unlikely, but more likely outcomes that offer continuity.
An example:
1. You suddenly wake up in your bed and it was just a dream. (Isn't that a convenient one? Who hasn't taken that route at least once already? Cheater!!!)
2. You get reborn and remember your previous life. This, too offers continuity. It's pretty unlikely - I mean physically a brain needs to form but somehow has the entirety - or at least some of - the memories of someone else that lived earlier -- but it's apparently likely enough on a cosmic scale, that with 8 Billion Humans on the planet, at any time you find at least a handful who claim to remember their past incarnations.
3. Other paranormal solutions. You could of course just wake up in some sort of afterlife that is elsewhere. Or everything turns out having been a simulation, or similar.
What can be ruled out is that you wake up in a universe where you don't exist, because, well... you don't wake up in any of those.
Now its important to keep in mind, this effect - if it's real - only protects your continuity, not that of anyone around you. Your loved ones can and will still die based on the likelihood of this happening in almost all timelines, and you can expect to end up in one of the more likely ones.
You could try something crazy, like - for example - trying to kill yourself whenever your loved ones die. Wouldn't that link your fate to theirs and put you always in a timeline where they survived too?
Sadly not. You might as well end up in one where you survived your suicide attempt as drooling vegetable and spend the rest of your - possibly eternal - life wishing you hadn't done that. Or you just end up in an afterlife -- alone...
Now the tricky question is -- can you rely on that?
Sadly not. All this effect guarantees is some sort of continuity. But it does not guarantee sanity or any quality of life. If in a timeline you live to 250, you might have so severe Alzheimer and dementia that you don't even remember who you are.
And also, this whole thought experiment revolves on the existence of alternate timelines and multiverses.
They are a convenient "cheat" to explain some quantum physical phenomenon, but they might not actually exist. There IS the odd chance that our timeline, our universe is in fact the only one, and/or there are no bifurcations that link ours with any other potential reality.
So don't make any silly practical experiments to put this to the test quite yet. After all, we all are gonna test this theory eventually, which is IMHO more than soon enough.