Yes and no. Your question seems to be in reference to this passage from Chapter V of The Scarlet Letter:
Throughout them all, giving up her individuality, she would become the general symbol at which the preacher and moralist might point, and in which they might vivify and embody their images of woman’s frailty and sinful passion. Thus the young and pure would be taught to look at her, with the scarlet letter flaming on her breast,—at her, the child of honorable parents,—at her, the mother of a babe, that would hereafter be a woman,—at her, who had once been innocent,—as the figure, the body, the reality of sin. And over her grave, the infamy that she must carry thither would be her only monument.
Hawthorne continues to speculate upon Hester's motivations for remaining when she could easily leave the Massachusetts community and resume her life:
But there is a fatality, a feeling so irresistible and inevitable that it has the force of doom, which almost invariably compels human beings to linger around and haunt, ghost-like, the spot where some great and marked event has given the color to their lifetime; and still the more irresistibly, the darker the tinge that saddens it.....The chain that bound her here was of iron links, and galling to her inmost soul, but never could be broken.
Thus subjugated to the Puritanic gloom of the colony, because of her sense of obligation, Hester's essence "withers like an uprooted weed left in the sun." This is why Hester's hair has lost its luminousness; she is compromised between independence and conformity by her punishment. While Hester's corporal being remains in the Puritan community, albeit ostracized to the edge of the village, her spirit yet emerges as she retains her fierce independence. For, she accepts her status, but she does not accept the guilt attached to her sin; she has become more independent and pensive. In Chapter XIII, for instance, because she is so often alone, Hester ponders the role of women in her society and decides that men must change their perception of women, while women must assume a more assertive and independent rold. Hester concludes, that "[T]he world's law was no law for her mind." She then wonders if existence is worth accepting, "even to the happiest among them?"
At times, a dark and grand doubt affects her soul, whether it were not better to send Pearl at once to Heaven, and go herself "to such futurity as Eternal Justice should provide." Clearly, as Hawthorne writes, "The scarlet letter had not done its office." Hester is not reformed by her punishment; she has merely been altered. Yet, her fatalistic attitude about herself brings her back to the community after she has gone with Pearl back to England. Standing in the doorway of her lonely cottage, Pearl stoops and reclaims the worn scarlet letter, placing it again upon her bosom. She feels the "force of doom" and yields to the stultifying Calvinistic Puritanism that doles punishment to those of good works if they have transgressed, but her spirit remains independent.