TL;DR: I have solved aging and cancer with the power of handwaving and genetic science. All rejoice.
Yes, there is a question at the end of this all, but you have to read it for it to make sense.
In order to provide context for this question, I had to write a wall of text to explain the specific mechanism of how my version of biological immortality works, since that mechanism is relevant to the question. I think it's around a 5 on the (WARNING: TVTROPES LINK) Mohs Scale Of Science Fiction Hardness (WARNING: TVTROPES LINK).
Living things age. This is a fact. A specific component of the process of a living thing aging is the shortening of the telomeres in that thing's cells.
Telomeres are non-coding DNA - more commonly known as junk DNA. This type of DNA cannot code for proteins, meaning that it is functionally useless. The function of telomeres is to essentially act as an ablative shield for the rest of the chromosome they're attached to; each time a cell replicates, a little bit of the telomere is worn away, because the replication process is not 100% accurate/efficient. However, as a telomere wears down, the organism it's a part of is unaffected, since it's not the coding DNA being damaged. Once the telomeres are all burned out, actual DNA stops being replicated effectively, and the cell soon fails to replicate.
Think of it this way: you have a magic copier capable of copying an entire stack of papers at once, and you have a lot of papers you need to copy - each one of them is vital for your job, and you'll get fired if enough of them are lost. However, each time the copier copies, it folds, spindles, and mutilates the topmost paper and the bottommost paper in the stack. The solution to that is to put in sacrificial papers on the top and bottom of the stack; these don't actually carry any information. However, after repeated copying, they eventually run out, and then the copier starts destroying paper with information on it, and you get fired.
This means that cells have a set replication limit - once they replicate enough times, they run out of telomere, and then they crash and burn. Over time, this eventually leads to bodily structures failing as their cells break down. This is aging.
However, there's a reason your body has telomeres, other than to cause depressing funerals, and it's an ugly one - cancer, a self-replicating blob of cells. Telomeres stop cancer cells from replicating out of control; they're essentially an automated self-destruct switch, and many cancers are likely never noticed by humans, since they fizzle out and die before getting really big - the telomeres stop them from making more of themselves ad infinitum. Only the biggest and meanest cancers make it to the killing-you-horribly phase thanks to telomeres.
This means that, while biological immortality is certainly an exceptionally appealing target for lots of research, you're not going to get it by removing the ability of the telomeres to shrink. While that'd stop aging, it'd also allow even the smallest cancers to replicate end-over-end until you're some kind of disgusting, gristly blob straight out of Warhammer 40,000, which will probably kill you long before old age would have (and in a much more unpleasant fashion, to boot!).
But, y'see - and this is the thing for any self-respecting hard sci-fi writer, as well as any self-respecting seeker of immortality - as of currently, eternal telomeres are one of our best bets at biological immortality. You can't have old age without telomeres, because, without them, your cells break down and you die. But you can't have invulnerable telomeres - ones that never wear down - because then you get cancer-inated.
What's a person to do?
Well, y'see, here's the solution: instead of making invulnerable telomeres, you constantly add onto them. They regenerate. They never run out.
"But - how?" the StackExchangians ask.
Well, this is how. CRISPR-Cas9 genome editing is amazing - it deserves more than a Nobel prize. We can manipulate the fundamental building blocks of life. We are GODS. Well, not quite, but you get the point.
Thing is, CRISPR-Cas9 can add to strands of DNA. Telomeres are strands of DNA. It can probably add to telomeres forever, actually. As the telomeres wear down, CRISPR-Cas9 slaps more DNA onto the end. The cells never age, because they never run out of telomeres. Aging is dead, and humanity has killed it. Bwah-hah-hah.
Now, figuring out how to integrate the processes of CRISPR-Cas9 into the body is another story, but it's a story for later, and, frankly, is worthy of a handwave - albeit a believable one. But there's another problem.
"But - cancer!" the StackExchangians exclaim.
That's the trickier bit, but I'm a tricky-ass brain-piloting-a-muscle-and-bone-mecha, and so I concocted an even trickier solution.
DNA repair is, as Wikipedia so succinctly puts it:
a collection of processes by which a cell identifies and corrects damage to the DNA molecules that encode its genome
Key word: identifies. The cell can tell between normal and abnormal.
Let's backtrack a bit - back to cancer.
Cancer cells are so awfully successful because they're good at getting around your immune system - to your immune system, a set of cancer cells look just like yet another set of your body's cells. Nope, nothing to see here, officer. Move along. Ignore the fact that there are more of us than there were a minute ago.
But what if the body could tell the difference? It'd kill the little bastards dead if it could tell the difference. But, unfortunately, it can't.
But, with my idea, it can.
Y'see, that CRISPR-Cas9 thing - it constantly adds more DNA to telomeres. This happens each time a cell replicates, so that the telomeres never shorten. It doesn't take long for cells to replicate. This means that, with CRISPR-Cas9 fully armed and operational, what the telomeres are made out of is constantly changing, since what they're made out of changes each time they replicate. Moreover, that change doesn't repeat for a long time - this weird, integrated-into-the-body CRISPR-Cas9 system just grabs the piece of the telomere that breaks off during cell replication and slaps it back into the base of the telomere as replacement material. Eventually, it'll come back up again, but by that time, all the cells in the body will have already gone through that configuration of telomeres (more on that later).
In other words, the makeup of the telomeres constantly changes. Moreover, and this is critical: this occurs as a body-wide process - i.e. every single telomere in the body goes through the same configuration eventually. This is not a handwave - remember, CRISPR just takes the bit that broke off the end of the telomere and puts it back at where the telomere connects to the DNA. It's always the same telomere, and not a bit of it changes - it's just that CRISPR rearranges it every time the cell splits. It might change at a different rate, depending on the type of cell in question, but it changes regardless.
Now, there is a way for the body to find and exterminate cancer. How? It looks for out-of-date telomeres. After all, cells replicate quickly, meaning that the telomeres change in composition quickly - the telomeres of 8:00 at night are different from the telomeres of 8:00 in the morning. Certainly, some cells replicate more quickly than others, meaning that differences in what's "up to date" will form (i.e. brain cells are on a different telomere than bone cells, etc.), but the solution to that is for the cells of each bodily tissue's CRISPR-Cas9 process to use a different adeno-associated virus (below) to repair its telomeres - one for the muscle cells, one for the brain cells, one for the bone cells, etc.
Basically, each type of bodily tissue runs on a different "clock", which is separate from all the "clocks" the other bodily tissues run on. This ensures that the immune system doesn't kill off cells that grow more slowly than others.
However - and this is the second handwave, other than CRISPR-Cas9 being integrated into normal cellular biology - this CRISPR-Cas9 process refuses to work with cancer cells. Somehow, it identifies them and refuses to add onto their chromosomes. This means that cancer cells age like normal, while the body's cells are immortal. This, alone, resets the cancer rate to a normal human - while eliminating aging.
But there's more.
Remember that bit about how the cell can tell between normal and abnormal, and the bit about how the telomeres of 8:00 at night are different from the telomeres of 8:00 in the morning? Well, I bet you that the body can apply the ability to tell between normal and abnormal to telomeres. A third handwave, but still 100% plausible.
This means that the body can separate the telomeres of 8:00 in the morning from the telomeres of 8:00 at night. It'll do this by using the slowest-reproducing cells as a reference; after all, those are the last ones to "roll over" to the next telomere configuration, meaning that all the other cells do so beforehand, and, therefore, any cells drifting around with out-of-date telomere configurations must be cancerous, and not just ones that replicate slowly.
Let's say it's 8:00 at night. The skeletal muscle cells are running on the most recent, "up-to-date" generation of telomeres - except for a little clump of cancerous skeletal muscle cells, which went rogue at 8:00 this morning and aren't. They're still stuck with the morning's revision of telomeres, since the CRISPR-Cas9 refuses to update them.
And, with the body's ability to tell between the cells of 8:00 AM and 8:00 PM, those cancer cells stick out like a sore thumb. They are not like normal, real-life cancer cells, which blend in and grow and expand - they are very clearly out of date in comparison to the rest of the skeletal muscle cells, by 12 hours.
They are rapidly exterminated.
So, not only does this cure cancer - it cures aging, AFAIK. And all it needs is three handwaves.
With all of the above in mind, I finally present the question you've all, I'm sure, been dying to answer:
How long will can a 100% cancer-immune person live if they no longer age via cell death?
Assume that they have a healthy diet, plenty of access to sunlight, are at no risk of injury, etc.
Like, I'm sure they'll somehow die eventually, but the odds are that it'll take a heckin' long time.
Also, AlexP kindly pointed out that neurons do not replicate. However, that doesn't mean that the CRISPR-Cas9 process won't constantly shuffle the telomeres of neurons anyway in order to keep up with the rest of the cells and avoid deletion.
