In Plato's Laws, the punishment for husbands killing wives and vice versa is permanent exile from their homeland. Fratricide, Matricide, and Patricide receive the death penalty. From a modern vantage point it would seem that exile is the lesser sentence, but for those in the dialogue, it is much worse. Part of the reason is likely due to certain beliefs about the afterlife--that a murdered soul will continue to inhabit the land where he dies, and thus torment the soul of his murderer. Thus, an exile that dies outside of its homeland must wander not only in life but also in death--permanently separated from the soil from everything that mores his identity and purpose--homeland, people, ancestors, progeny.
In this observation the punishment of exile seems much closer to the Christian idea of eternal damnation--the torment of being forever exiled from the God who gives identity and purpose to all that He has made. To be exiled in the second death is indeed a fate worse than death itself. The immortal soul destined to wander without identity or purpose seems torment enough--to be left alone, entirely alone, knowing that you abandoned your only hope of restoration would be a torment akin to a lake of fire for the soul.