At the end of Oedipus Rex, Oedipus blinds himself, and he asks for his daughters, Antigone and Ismene, to be brought to him. It's interesting that he doesn't ask for his sons, Eteocles and Polyneices; although, as he explains to Creon, they're men, and they can fend for themselves in the world.
OEDIPUS. I reck not how Fate deals with me
But my unhappy children—for my sons
Be not concerned, O Creon, they are men,
And for themselves, where'er they be, can fend.
But for my daughters twain, poor innocent maids,
Who ever sat beside me at the board
Sharing my viands, drinking of my cup,
For them, I pray thee, care, and, if thou willst,
O might I feel their touch and make my moan.
Oedipus is concerned that his daughters won't be treated well in life because he's their father and brother, and they'll likely suffer more than their brothers because of the curse and the disgrace Oedipus brought to his family.
OEDIPUS. ...Though I cannot behold you, I must weep
In thinking of the evil days to come,
The slights and wrongs that men will put upon you.
...Who then will wed you? None, I ween, but ye
Must pine, poor maids, in single barrenness.
...To you, my children I had much to say,
Were ye but ripe to hear. Let this suffice:
Pray ye may find some home and live content,
And may your lot prove happier than your sire's.
When Sophocles wrote Oedipus Rex, he knew quite well what was going to happen to Antigone and Ismene, because he'd already written a play about them. Sophocles wrote Antigone in about 441 BCE, twelve years before he wrote Oedipus Rex. Sophocles also wrote Oedipus at Colonus, the third of the "Theban Plays," shortly before his death in 406 BCE, and it was performed at the Festival of Dionysus in 401 BCE.
Sophocles wrote the plays out of order. Chronologically, the events in Oedipus Rex actually occur first, followed by the events of Oedipus at Colonus and then by the events in Antigone.
After the events of Oedipus Rex, Oedipus and his four children live in Thebes until the children are young adults. Oedipus then exiles himself to Colonus, and he takes Antigone with him to care for him as he grows old. Ismene, Eteocles, and Polynices stay behind in Thebes. Creon steps down as king, and Eteocles and Polyneices agree to share the throne of Thebes.
As Oedipus at Colonus begins, the arrangement between the brothers has lasted for about a year, until Eteocles decides that he doesn't want to share the kingdom anymore and that he won't give up the throne when it's Polyneices turn to be king. This causes a civil war between the brothers.
Ismene travels to Colonus to tell Oedipus and Antigone about the problems in Thebes that have led to a civil war. Oedipus curses both brothers, and Oedipus refuses to talk with Polyneices, who has travelled to Colonus to ask for Oedipus's support in his war against Eteocles.
Oedipus relents and agrees to talk with Polyneices but becomes enraged at him. He tells Polyneices that he deserves his fate and prophecies that Polyneices and Eteocles will kill each other in the civil war. Polyneices returns to Thebes.
Oedipus dies and is buried in Colonus, and Antigone returns to Thebes.
As Antigone begins, the civil war in Thebes has ended, and, as Oedipus prophesied, Eteocles and Polyneices kill each other in the war. Creon is king of Thebes again, after the deaths of Eteocles and Polyneices, and he decrees that Eteocles will be accorded a hero's burial because he fought on the side of Thebes. He also decrees that Polyneices must be given no burial, under pain of death, and that his body must be left in the desert.
Antigone disobeys Creon's decree, and Creon condemns her to death. Ismene disappears from the play after Antigone is sentenced to death, and no further mention is made of her.
Creon has a change of heart—after being threatened with various horrors by the gods—but Antigone kills herself in the cave where she was buried alive before Creon can release her.
In summary, Oedipus's children Eteocles and Polyneices kill each other, Antigone dies in a cave, and Ismene apparently survives.
There is a further myth attached to Ismene, in which Ismene is betrothed from childhood to Atys, the son of Croesus, king of Lydia. Atys fought and died in the civil war in Thebes in which Eteocles and Polyneices killed each other.
Tydeus, the man who killed Atys in the war, later killed Ismene at the instigation of the goddess Athena, who was jealous of Ismene and upset with her for making love with Theoclymenus, a prophet from Argos.
In all, Oedipus's children all suffered fates worse than his own, as Oedipus feared and predicted and as the gods decreed.