What does the fact that Hester remained in the town and bore her shame tell us about her character?

Hester is strong willed and persistent. She isn't going to walk away in shame, so instead she stays and supports both herself and her daughter.

"Though she is free to leave Boston, she chooses not to do so. She settles in an abandoned cabin on a patch of infertile land at the edge of town. Hester remains alienated from everyone, including the town fathers, respected women, beggars, children, and even strangers. She serves as a walking example of a fallen woman, a cautionary tale for everyone to see. Although she is an outcast, Hester remains able to support herself due to her uncommon talent in needlework. Her taste for the beautiful infuses her embroidery, rendering her work fit to be worn by the governor despite its shameful source. Although the ornate detail of her artistry defies Puritan codes of fashion, it is in demand for burial shrouds, christening gowns, and officials’ robes. In fact, through her work, Hester touches all the major events of life except for marriage—it is deemed inappropriate for chaste brides to wear the product of Hester Prynne’s hands. Despite her success, Hester feels lonely and is constantly aware of her alienation. As shame burns inside of her, she searches for companionship or sympathy, but to no avail. She devotes part of her time to charity work, but even this is more punishment than solace: those she helps frequently insult her, and making garments for the poor out of rough cloth insults her aesthetic sense."