I understand that identification of "Will to live" as physical substance would be probably what would sell the concept if executed well.
That's not what I meant. I was staying that in-universe, it would be hard for the Foundation to empirically determine that "will to live" is being turned into a physical substance. Explaining that doesn't really sell the concept—plenty of anime have already done that, like the dying will flame from Katekyo Hitman Reborn! and I think Buso Renkin. And so on. It's kind of a silly overdramatic sort of presentation.
The main reason this thing can kill is that if something does not have will to live, it just don't live. Thus ceasing life functions
I think you misunderstood my question. I'm asking why this thing needs to kill at all. It certainly doesn't seem to benefit much from it, and besides, it's just a statue.
If the only reason this thing exists as it is is that you want to write about a thing that kills people in a convoluted way, that's not enough of a narrative to carry it.
The cells in subjects body cease their function to support live cause they themselves have will to do so. So a cell by cell subjects body commit suicide.
…You should probably do some more research into cell biology if you really want to go this route. This isn't how cells work at all, and attempting to have an in-universe scientist propose this as an explanation will just break suspension of disbelief.