Fight! Fight Fight!
Pygmalion ends with a bang, not a whimper.
Here's what goes down: Henry and Eliza have a huge fight. Eliza's already made Higgins plenty angry by leaving his house, and then proceeding to act all cheery and nice the next day. She's already given Pickering most of the credit for her transformation from flower girl to lady, and now, to top it all off, she's refusing to come back and live with Higgins.
You see, Eliza doesn't know what to do with herself now that she's got an upper class accent, but no money, and no place to go.
Higgins doesn't seem too fazed by this. He tells her that, no, he doesn't mean to treat her poorly. He treats everyone poorly. It's just his way of being fair. Then, for good measure he calls Eliza a liar, a fool, an idiot, a "damned impudent slut" (5.263), and—oh, yeah—and he almost strangles her.
Eliza doesn't buy a lot of what he's saying. She doesn't seem convinced by the whole "I treat everyone like garbage" excuse. She's insulted by Higgins's offer to arrange a marriage with somebody rich. She's so annoyed by the whole thing that she starts making threats of her own. She tells Higgins that she'll marry Freddy if she has to (Higgins doesn't want his "masterpiece" wasted on such a lout).
She even threatens to use her knowledge against him, to teach one of Higgins's competitors the methods she learned or—and this really ticks him off—to go into business for herself.
Cruelty = Equality (When You're Henry Higgins)
Higgins then has a great realization. By finally learning to treat him poorly, Higgins believes that Eliza has finally become his equal. Again, this all seems a bit off, and Eliza herself isn't convinced. And why should she be? She has plenty of reasons not to trust him—the guy just tried to wring her neck.
Eliza turns around to leave, telling Higgins,
LIZA: I shall not see you again. Good-bye. (5.270)
Higgins isn't one to give up, however. He calls after her and tells her to pick up some groceries and fresh clothes. Higgins's mother, who's just come in to get Eliza, thinks he's crazy, but Higgins himself is sure.
HIGGINS: She'll buy em all right enough. Good-bye. (5.275)
Those are the last words, leaving a lot up in the air. Higgins is sure Eliza will come back but, well, he's been wrong before. Eliza seems to doubt the sincerity of Higgins's arguments, but on the other hand, he can be pretty persuasive. She's still left in a difficult position: she can't go back to selling flowers, but she doesn't want to marry into money. And Higgins won't meet her halfway…at least not yet.
Is there romance in the cards?
Pygmalion 2: 2 Pyg, 2 Malion
Not according to Shaw. He wrote a "Sequel" to Pygmalion and, like most sequels, it's not nearly as good as the original. It's just a really long explanation of what happens—Shaw just wants us to know that everybody reading the play is silly and sentimental, and, no, Higgins and Eliza don't ever smooch. Instead, she marries Freddy and they open a flower shop.
The sequel closes with the lines:
[...] [Eliza] likes Freddy and she likes the Colonel; and she does not like Higgins and Mr. Doolittle. Galatea never does quite like Pygmalion: his relation to her is too godlike to be altogether agreeable. (Source)
We here at Shmoop say forget about the sequel and go with your gut. You can do better than that.