In Henrik Ibsen's, A Doll's House, and George Bernard Shaw's Pygmalion, both Nora and Eliza go through a major transformation, which ultimately changes each woman.
Nora is married to a man (Torvald) who treats her like a child. He has little regard for her as a person, and she seems happy with this for a time. However, Nora is responsible for [illegally] borrowing money to pay for a trip to a warmer climate that saved Torvald's life some time ago.
When Torvald finally learns what she has done, he expresses no thanks for saving his life, or concern over how hard she has had to work to pay the loan back. All Torvald cares about is his reputation, and how he will be judged based on what his wife has done. It is at this point that Nora decides she cannot be a wife or mother in Torvald's house, and she leaves him at the end of the play.
Eliza Doolittle works in the marketplace selling flowers. She is unkempt and something of a con-artist as well. She becomes a person of interest to Henry Higgins, a man who studies speech patterns based upon where a person has been raised. When Eliza shows up at his door asking for elocution lessons, Higgins and his new acquaintance Colonel Pickering, decide to enter into a wager to see if Higgins can pass Eliza off as a member of the aristocracy based upon her speech, as he boasts.
The "experiment" proceeds, but Higgins has no thought of what will become of Eliza when they are done, for she will not longer be suited to sell flowers, and will, therefore, have no way to support herself. After Higgins and Pickering agree that the experiment has been successful, neither recognizes that Eliza played any part in their achievement, and neither congratulates her on what she has accomplished. Eliza storms out, and decides she will marry Freddie, a member of the ton.
Higgins goes searching for the missing Eliza, who has gone to Henry's mother's flat. When he discovers her there, it seems as if she will leave him. However, he explains that his behavior is nothing personal: he simply acts the same way with everyone. Eliza decides to stay. Higgins expects that she will continue to see to the keeping of his home, as she has been doing for sometime, and the play ends.
By way of comparison, both women are regarded with little respect by the men in their lives. Nora assumes the responsibilities of a wife; Eliza assumes the responsibilities for learning, and caring for Higgins and his home. Both women find themselves changed by the circumstances of each woman's life.
However, in terms of Nora's growth as a person, she is convinced that she can no longer live with her husband, someone she does not know at all, even though they have lived together for many years and have children. Nora's change forces her to see herself and the world she lives in, in a new light, and she departs at the end of the play.
On the other hand, Eliza's growth as a person is something that improves her sense of self, making her more demanding of Higgins' respect. Whereas Torvald cannot convince Nora to stay, Eliza's situation is different, and Henry's candor and seeming appreciation for the changes she has gone through, convince Eliza to stay. In sharp contrast, there is nothing Torvald sees in the new Nora that moves him to praise her in any way.
Nora changes and finds she cannot live the life of her former self. Eliza changes, and discovers that as long as Higgins is willing to see her as a person deserving of his respect, she will stay.