There probably won't be a cure for death without the problems outweighing the benefits. The only immortal biological species is the hydra (technically they are not immortal since things like predators and pollution can kill them). But one gene can affect multiple seemingly unrelated traits because in the case of an experiment by former geneticist Dmitri Belyaev who was forced out of his job as a geneticist by Niken Khrushchev who ruined soviet agriculture and genetics. Dmitri was forced to breed foxes, selecting them for tameness. Even though he and his team of breeders were breeding only for tameness many other traits were affected (being able to put their ears down, wagging their tails when happy, and barking like domesticated dogs, mottled fur, a raised tail, ears being floppy for a few months after being born, and coming into heat every six months instead of yearly).