one becomes immortal through recognizing the unity of all things. the realization that the boundary and distinction between you and the whole of creation is illusory leads to the awareness that your own “death” is not a death because the life force and energy that lives within you will still yet live on when you perish. “you” will be resorbed into the Earth, into creation, living on.
this is what is behind the saying “he who dies before he dies does not die when he dies.” you die to your own ego identity and see clearly that you are a part of something much larger than yourself. death, in this way, is an illusion. you do not exist — the illusion of selfhood is the illusion of Maya.
maybe “we” can’t die because “we” never existed in the first place. if death is an illusion, then so is birth; if birth is an illusion, then so is death.