Hester Prynne is one of the two primary characters in The Scarlet Letter by Nathaniel Hawthorne, and she is the wearer of the scarlet letter. After Arthur Dimmesdale dies, Roger Chillingworth has no reason to live, and he dies within the year. Soon after Chillingworth's death, Hester and Pearl actually do leave New England
[T]he wearer of the scarlet letter disappeared, and Pearl along with her. For many years, though a vague report would now and then find its way across the sea,--like a shapeless piece of driftwood tost ashore, with the initials of a name upon it,--yet no tidings of them unquestionably authentic were received.
One day, without any warning or fanfare, however, Hester returns alone to her small house near the water.
So perhaps a better question is why she left England and came back to this place which had known her shame. Of course she did not have anything substantive to draw her back here: no friends, no real connections of any kind. Yet she returns and resumes wearing the scarlet letter, despite the fact that no one would ever have required her to wear it. Pearl stayed in England (happily married and now "normal," from all accounts), and Hester could have stayed there, too.
Hawthorne tells us why Hester came back to New England.
[T]here was a more real life for Hester Prynne, here, in New England, that in that unknown region where Pearl had found a home. Here had been her sin; here, her sorrow; and here was yet to be her penitence. She had returned, therefore, and resumed,--of her own free will, for not the sternest magistrate of that iron period would have imposed it,--resumed the symbol of which we have related so dark a tale.
Hester came back here because she has a connection to this place because of Arthur and Roger and her sin. She obviously feels inextricably connected to this place for complicated reasons--love, hate, shame, guilt--and this, of course, is where she dies and is buried.