In Antigone by Sophocles, Haemon is the son of Creon and engaged to marry Antigone. Creon has issued a proclamation that any person caught burying Polyneices will be stoned to death, as he considers Polyneices a traitor to Thebes.
Antigone, however, is the sister of Polyneices (and daughter of Oedipus). Within Greek religion, women had a strict obligation to conduct certain female-specific burial rituals for their male relatives. Thus Antigone feels that she has an inescapable religious duty to conduct a burial, by sprinkling dirt on the corpse and singing lamentations. To shirk this duty, as she says, would bring down the wrath of the chthonic (underworld deities) upon her. When she is caught, Creon confronts her and she defies him. After she is condemned by Creon, Haemon speaks to Creon attempting to defend her, but Creon is obdurate and threatens to kill Antigone in front of Haemon. Haemon responds by saying:
She’ll not die with me just standing there.
And as for you— your eyes will never see my face again.
After this speech, Haemon exits and kills himself offstage. The chorus and then Creon receive this news by means of a messenger.
Once Antigone refuses to participate in Creon's plot, the stage is set that will lead to Haemon's death. Enraged at her unwillingness to go along with his plans, Creon declares that Antigone must die for what he considers treason. Eventually, after seeing the suffering of his people and discussing the reasons behind all the trouble with Tiresias, he agrees that he ought to have mercy on Antigone and release her.
Unfortunately it is too late and he discovers, as he goes to release her, that she has killed herself. Haemon, broken-hearted at his mother's death is there weeping at her side and when Creon and his men arrive, Haemon kills himself out of grief and anger at what Creon has brought upon his family and his people.