In "A Doll's House," does Nora succeed or fail after becoming an independent woman?
In my opinion, Nora does succeed at the end of the book. And here is why: she succeeded in hiding the fact that she borrowed money to help her husband when he was sick and they needed money to travel to Italy, and she has secretly worked to earn money to pay back the loan. This is evidence that she is capable of being on her own.
And, second, the very act of leaving, is a success. She walks out knowing full well that she is alone, but she is resourceful enough to make it on her own. Nora is determined and ready to be on her own so I think it is safe to project that Nora will succeed. Her life won't be easy, but she will survive and lead a full life.
Ibsen does not tell us Nora's fate--the play ends with the sound of the front door shutting after Nora leaves Torvald. Given the cultural climate of nineteenth-century Norway, one can speculate that a woman may had a tough time making her own way in a world where she has few rights and no legal status. The text only offers evidence that Nora has become an independent thinker, nothing more.
Nora does seem to succeed at becoming an independent woman, for she develops into a woman with her own thoughts and actions. Seeing Torvald's manipulation of his household and Nora realizing the lie she has been living all her years of marriage, she overcomes the stereotype Torvald and her father molded her into. Distancing herself from her home shows her first steps of becoming an independent woman, despite the difficulties she might go through, given the situation of woman's status in that period of time.