Symbolism of the Dead Letter Office

The Dead Letter Office where the narrator discovers Bartleby was formerly employed is symbolic of the existential demise that humans will ultimately reach: death. Bartleby sorts letters in the office pointlessly "for the flames" (34), and in doing so heightens his "pallid hopelessness" (34) for life. The narrator surmises that the reason Bartleby preferred not to do things was because we are all going to die eventually so there's no point. Melville is saying that the letters in the office "speed to death" (34), just like Bartleby and the rest of humanity. The dead letters are like Bartleby in that nobody wanted either of them, and so each was sent to their respective office, essentially to die.