opening scene of the play, but there's noforeshadowing about the means of her death.

ANTIGONE. Say I am mad and give my madness rein
To wreck itself; the worst that can befall
Is but to die an honorable death.

Creon, too, foreshadows Antigone's death in his scene with his son, Haemon, who threatens to kill himself if Creon doesn't release Antigone from the cave where Creon ordered her sealed up to die.

CREON. Off with the hateful thing that she may die
At once, beside her bridegroom, in his sight.

Antigone's suicide comes as somewhat of a surprise to those who don't know the ancient myths surrounding Antigone, which Sophocles closely followed in Antigone.

Interestingly, Euripides wrote a play entitled Antigone about twenty years after Sophocles's Antigone. The basic plot of Euripides's Antigone is similar to Sophocles's Antigone, but the plays differs significantly with regard to Antigone's fate.

Although only fragments of Euripides's Antigone exist, scholars have determined from the contemporary writings of Aristophanes of Byzantium and other sources that Euripides wrote in his version of Antigone that Haemon was discovered with Antigone trying to bury Polyneices.

After Antigone and Haemon are apprehended burying Polyneices body, Creon decrees that Haemon must kill Antigone. Haemon appeals to the god Dionysus to spare his and Antigone's lives, and Dionysius appears deus ex machina to intercede with Creon on their behalf, and their lives are spared. The question of Antigone's suicide never arises in Euripides's Antigone, but that's not to say that Antigone and Haemon wouldn't kill themselves if Dionysus refuses or otherwise fails to save their lives.

There's also the question of what constitutes an "honorable death," as Antigone calls it.

Aristotle wrote in Ethics, that except in very few instances, taking one’s own life to avoid poverty, desire, or pain is cowardly.

The law does not expressly permit suicide, and what it does not expressly permit it forbids (Ethics, XI).

Aristotle writes further that suicide is an act against the state, and that there is "a certain infamy is attached to the suicide as to one who acts unjustly towards the state" (Ethics, XI).

Sophocles wrote Antigone in about 440 BCE, about a hundred years before Aristotle wrote Ethics, so attitudes towards suicide might have changed in the interim. For example, Aristotle, along with Plato and other philosophers, believed very strongly in free will, whereas a belief in fate and the will of the gods prevailed when Sophocles wrote Antigone. Antigone and other plays of the ancient Greek period were written to reinforce those beliefs.

Antigone is definitely not cowardly, even though her suicide was an act against the state, which she no doubt intended it to be. It was also an act of free will in denying the state ultimate control of her life.

Aristotle and Plato believed, however, that suicide was morally acceptable when the gods gave a sign that a person had achieved what they had been put on earth to achieve.

No one knows what happened inside the cave, but Antigone might have decided, or been told by the gods, that she had achieved her purpose on earth and fulfilled the will of the gods by burying Polyneices—which Antigone asserts in the play is her reason for defying Creon's decree.

ANTIGONE. Yea, for these laws were not ordained of Zeus,
And she who sits enthroned with gods below,
Justice, enacted not these human laws.
Nor did I deem that thou, a mortal man,
Could'st by a breath annul and override
The immutable unwritten laws of Heaven.

By this standard, Antigone died an "honorable death."

Antigone hangs herself in the cave (tomb) where she has been buried alive to slowly die of starvation. She commits suicide for several reasons. First, she is a devoutly religious person who puts her religious faith ahead of her own life. Her religion tells her Polyneices must be buried, and so she covers him with dust in defiance of Creon. This sets into motion the events that end up with her being buried alive.

By the time she kills herself, she is in a state of grief, she is cut off from her community, and she sees no hope for her future.

In hanging herself, Antigone regains a measure of control over her fate. She decides when and how she will die.

Finally, her suicide is an act of defiance. Just as she disobeyed Creon in "burying" Polyneices, she again defies him and makes a political statement by refusing to let him control her. It is significant to her faith because it shows she does not accept Creon's decree that it was wrong to obey the gods and bury her brother.

Antigone's suicide is in keeping with the fatal and fatalistic atmosphere that surrounds her entire family. She professes devotion to her family, the doomed house of Oedipus. With the exception of her sister Ismene, they have all preceded her in death: her father, mother and two brothers (who killed each other); it seems fitting that she join them in death. As Creon tells her brutally at one point: 'Go and share your love with the dead'. She prefers to do that rather than go on living in a world which is largely meaningless to her. She has been entombed alive, but she prefers to hasten her end rather than wait for it.  

Antigone dares all for her family, and sacrifices all. She had earlier accompanied her blind, disgraced, exiled father Oedipus, and then she buries her brother Polynices, whose corpse had been left exposed as he was deemed a traitor. By this latter action she ensures her own condemnation by the state. For this action she sacrifices her own life, her own hopes for marriage and children - she was betrothed to Haemon, son of Creon, the ruler who officially condemns her. She bewails this loss but does not waver from her preferred course of action.

Antigone is heroically dedicated to her ideals and carries them out to the letter. Her devotion to family and family duties is an all-consuming passion with her. She is utterly inflexible and and determined, one of the most towering characters in all of ancient Greek tragedy. Her suicide is one final act of defiance against the world that condemned her for carrying out her family duty in burying Polynices. 

When Antigone refuses to obey the order of Creon to not bury her brother’s body, she makes what is in our world a political protest against what she considers an unjust and immoral law. Her refusal to obey Creon's edict to leave her brother's body to be consumed by wild animals leads to her capture and to her death.  Although Creon decides to execute Antigone, he later agrees to set her free because the “mob” wants her to live.  She could then, escape death. By taking her own life (she hangs herself), she again refuses to submit to Creon demands.  Although she ends her life, she does so on her own terms, not on his.