Antigone is sentenced by Creon to be buried alive in a stone cave, used as a tomb, far away from the city. He gives her enough food so that she can live a while longer inside the tomb. Ultimately, she will starve to death. According to Greek philosophy, starving to death would not be considered murder; therefore, Creon would be free of the guilt of having murdered Antigone and also free of "polluting" the city (See foot notes, eNotes etext line 790). We especially see Creon expressing his plans and his reasoning behind his plans in the lines:
I shall take her to a place completely
devoid of human life and hide her, living,
in a rocky cavern. I'll put in with her as much food as will ward off a curse, so that our city will escape pollution. (786-790)
The idea that Creon would be freed from pollution by killing Antigone in this manner stems Greek thought that any crime, both divine and human, offends the gods. Not only would murder be considered offensive, but also neglecting to give someone proper burial. Giving proper burial was seen as a cleansing ritual that not only purified the place of death of any unhealthful bacteria associated with death, restoring the place of death back to a healthful state, but honored the deceased (See notes, eNotes). Neglecting to give proper burial was seen as "an insult to human dignity" ("Death, Burial, and Afterlife in Ancient Greece"). Traditionally, the women relatives of the deceased were the ones who performed the burial ritual, including cleansing, anointing the body with oil, and dressing it, which explains why Antigone is so incensed that Creon will not even let her and Ismene tend to their brother's burial ("Death, Burial"). In addition, the Greeks believed that "punishments and pleasure" were doled out in the afterlife according to the person's deeds, which also explains why Antigone is concerned about offending the gods by not seeing to her brother's burial and Creon is concerned about offending the gods with Antigone's murder ("The Great Unknown--Some Views of the Afterlife").