Why is it taken for granted that life is always precious, as a whole, no matter what circumstances a person is in? Because it is finite, and unlikely to happen? Cancer often lasts for a finite duration, and is unlikely to happen. Why is it not precious, then, by the same reasoning?
I hypothesise the life is precious only if it feels to an individual person that it is precious. Never as a whole, because there is most likely no objective meaning or God to tell us what is worthwhile and what is not. What I mean by feel, is whether they think that their own life is precious or it matches up with their values to declare that life is precious.
Of course, there's probably no real definitive answer, because, as I've said before, you can't talk about subjective values on a universal scale, only on the scale of humans - and humans vary so intensely that it's hard to make sweeping generalisations. Life being precious for everyone sounds quite probabilistically untrue, as there are an extremely large quantity of ways you can arrange people so this life is precious, this life isn't etc. but only one way of all lives being precious. That's my simple analysis anyway. It could still be true, but is just quite unlikely. Life's inherent preciousness has no evidence for it as far as I can see, while life being given preciousness by subjective values has more evidence in that a lot of people DON'T treat their lives as precious (taking unnecessary risks - effective suicidality), which is odd due to the widespread meme of life's preciousness being ingrained into most people. What causes them to suddenly reject that? It's subjective evidence, but it's more than life's inherent preciousness has.
I've probably tied myself in knots doing this, and no objective values etc. makes things a lot harder and probably a lot more futile. Still, I don't like believing that my life is precious when it is quite clearly something that does not feel that way, which is hence why I personally reject any such claim. But that's based on absolutely nothing, so I'm still racking my brains trying to come up with something to refute something that sounds so baseless and intuitively wrong to me.