Hester Prynne is, certainly, a prime example of the fallen woman topos. At the beginning of the book, Hester is a young mother with a newborn baby. She has been alone in New England for two years because her husband, a wealthy scholar from England, had to stay in Europe to carry out some business. The mere arrival of a baby was sufficient evidence to convict her of adultery and make her become, in the eyes of New England’s puritan society, a fallen woman. If she wears a scarlet letter A on her dress it is precisely for all to see her guilt (Adultery).
It is important to notice that the narrator seems somehow inconsistent in his treatment of the fallen woman topos. First, he considers Puritan punishments too harsh, later he suggests that Hester Prynne has changed the meaning of the scarlet letter through her kindness, her diligence, and her hard work. Then, the narrator tries to convince us that Hester has been wandering in a moral wilderness. And when Hester returns to Boston at the end of the book –long after the death of both Dimmesdale and Chillingworth and after her stay with Pearl in Europe–, she voluntarily takes up the scarlet letter A. There are many possible explanations for why she acts in such a way, but the narrator offers the following interpretation: “Here had been her sin; here, her sorrow; and here was yet to be her penitence.” (24.11).
For more information, see J. P. Stout’s article in Bloom, H. (2004) Hester Prynne, Broomall: Chelsea House Publishers, pp. 167-180 (in Google books)