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.

Jocasta and Oedipus have four children: two boys, Eteocles and Polyneices, and two girls, Antigone and Ismene. Because Jocasta is Oedipus's mother, his children are also his siblings.

We know at the end of the play that Oedipus is worried about the fate of his two daughters, children he assumes will be unable to marry once their status as the offspring of incest is known. He asks Creon to care for them. The fate of his sons is left hanging. We find out in Antigone that Antigone and Ismene accompany their blind father from Thebes but return to the city. They find their two brothers fighting for the rule of Thebes. The two brothers kill each other, and Creon takes leadership of the city. Antigone gets into trouble with Creon for disobeying his orders, obeying the gods instead by burying Polyneices, whom Creon wanted to shame as a rebel by leaving his body exposed. She is sealed up in a cave by Creon and left to die. Creon has a change of heart, but it is too late: Antigone has already hanged herself.

Although none of this is spelled out at the close of Oedipus Rex, a sense of foreboding hovers over these children at the end of play because of their parentage. As we can see, three out of four quickly come to an untimely demise.

Oedipus and Jocasta have four children, two boys and two girls; Oedipus's children are also his half-siblings. Obviously this is a horrific truth, and of course neither Jocasta not Oedipus would have been in this relationship if they had known the truth. In Oedipus Rex by Sophocles, this truth is not revealed until the end of the play. 

When Jocasta realizes the truth, she hangs herself; when Oedipus realizes the truth, he gouges his eyes out as punishment and immediately demands even more punishment from his brother-in-law/uncle Creon, who is now king.

The blind, broken Oedipus calls for his children; when he hears crying, he knows they are his daughters (I'll just call them that, since it gets a little complicated to identify their relationship accurately every time I reference them) and he calls them to him. He says this:

      I weep for you. Although I cannot see,
      I think about your life in days to come,
      the bitter life which men will force on you.
      What citizens will associate with you?                                      
      What feasts will you attend and not come home
      in tears, with no share in the rejoicing?                                                
      When you’re mature enough for marriage,
      who will be there for you, my children,
      what husband ready to assume the shame
      tainting my children and their children, too?....
                                             
      Who, then, will marry you? No one, my children.
      You must wither, barren and unmarried.

The story ends before we can know whether the things Oedipus predicted came true, but we know that what he says is probably the girls' new reality. They will be treated as monsters by others and will have to endure shame and insults from everyone because of what Oedipus and Jocasta did. Oedipus is afraid that no one will ever want to marry them, which is probably true; and he sees a dire future of barren singleness for the daughters he loved. He does not say this, but remember that, until just a few moments ago, these girls were princesses, daughters of a king. Now they are the object of scorn, ridicule, and shame for all to see.

Oedipus then makes an appeal to Creon, both as king and as uncle to the girls:

      Do not let them live as vagrant paupers,
      wandering around unmarried. You are
      a relative of theirs—don’t let them sink
      to lives of desperation like my own.
      Have pity. You see them now at their young age                      
      deprived of everything except a share
      in what you are. Promise me, you noble soul,
      you will extend your hand to them. 

Notice that he asks Creon to take care of them, not to find them husbands or raise their social standing. This, Oedipus believes, is the best his daughters can hope for in these circumstances. His last words to the girls are as follows:

      pray that you may live as best you can
      and lead your destined life more happily
      than your own father.

We do not know, at the end of this play, what happens to his daughters; we do learn the fates of three of Oedipus's children in Antigone.