Other Educators have explored the various reasons that Antigone might have committed suicide, and the extent to which her suicide reflects her beliefs and ideals.
Antigone makes no mention of suicide at any time in the play. Antigone does foreshadow her own death in her conversation with Ismene in the opening scene of the play, but there's no foreshadowing 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."