While there is no real indication of what happens to Ismene, she does appear to survive the play. At the very least, there is no indication that she is actually dead.
Sophocles never returns to Ismene after she asks Antigone to let her die together with her sister. Antigone refuses; she doesn't believe that it's best for Ismene to die. Antigone is going to die because she decided to give her brother a proper burial; she doesn't think that Ismene should take the punishment when she was not brave enough to perform the deed that led to it.
Ismene's fate is not revisited. One can assume that she continued her life, though she was likely mourning for the people she loved. She was already in such despair that she was willing to die with Antigone. Therefore, she was probably even more unhappy once Antigone was gone and she was left behind alone.
Ismene doesn't have any part in the story after Creon decides that he is not going to kill her with Antigone. Her part—to be scared to bury her brother and...
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