The poem opens with the image of the Sybil of Cumae "hanging in a cage." The Sybil's immortality renders her unable to die, despite her intense desire to do so. In one sense, the Sybil symbolizes the fact that everyone in the wasteland is trapped in a cage that both is and is not of their own making, unable to die yet unable to live. In another sense, however, the Sybil is not like almost anyone in the wasteland since she "wants to die." An odd wish, given that men of every nation have sought out immortality for as long as we have recorded history. By death, the Sybil does not simply refer to the cessation of respiration in the "human animal." Rather, it is precisely the fact that death has become a biological event that makes the actual experience of death impossible from the outset! Furthermore, as the possibility of experiencing death is necessary to be human, men who can no longer experience death qua death are no longer exactly human. But they have not reached either deathlessness of the immortals or the eternal return of the animal. They are somewhere quite different.
The reason that Madame Sosostris does "not find / The Hanged Man" and cautions her querent to "fear death by water" is twofold. On one hand, she is a false prophet; precisely what is needed is "death by water," but as she is a sort of oracle of the wasteland itself, this is exactly what she will not counsel. On the other hand, her cards nonetheless speak the truth. All the forces and personages which are active in the wasteland are enumerated on her cards. The one that is absent - the Hanged Man - is the card that most directly deals with the possibility of properly dying.