No rational person believes such nonsense as "When you're dead you're dead." It might be the fact, and personally evident, that I am greater than the sum of my anatomy and its finitude. In a Nietzschean sense, it is a will to power to believe that when you're dead you're dead. Such people are looking for any excuse to destroy all that stands for the spiritual side of man. It is psychopathy at its worst.
Buddhism understands that what gives life and animates us is always outside of the animated psychophysical body including its death. It it also outside of thought and imagination; even our private internal dialogue. But more importantly, Buddhism teaches us that we can awaken to this beyond.
However, the worldly person (prithagjana) doesn't wish to recognize this because such a person is not noble (aryan). Unlike the noble, the worldly person doesn't care about ultimate truth. They are hopelessly caught up in the animated. It is like drinking Lethe such that the more one drinks the more they forget what is immortal—even how to reason.