To Live Forever is a science fiction novel by American writer Jack Vance, first published in 1956.
Medical technology has led to a great lengthening of the human lifespan, but, in order to prevent the Malthusian horrors of overpopulation, it is awarded only to those citizens who have made notable contributions.
A person whose lifeline reaches the vertical terminator is not merely deprived of life-lengthening treatment, they are deliberately eliminated by government operatives, known as "Assassins".
[1]The ultimate prize is the top category, called Amaranth, which offers true immortality to the fortunate few.
Galaxy reviewer Floyd C. Gale praised the novel as "frighteningly logical", saying that "[t]he sick, inbred society of Vance's imagination comes fully alive, even though his characters remain mere symbols.