Explain how/where Hester is buried and when she dies. Why might Hawthorne's message in allowing the story to end with Hester and Dimmesdale being remembered so ignominiously?

Soon after Dimmesdale dies, Roger Chillingworth also passes away. He leaves all of his estate to Pearl, who immediately becomes the wealthiest heiress in the New World. Hester and Pearl then disappear for several years. Hester returns to live the rest of her life in her cottage, and she becomes famous throughout the community for her help with the poor and sick. The narrator infers that Pearl is happily married and living overseas in Europe. Hester eventually dies and is buried in the cemetery at the site of the King's Chapel.

As for Hester, perhaps she feels the need to repay her debt of sin by helping the poor and the sick, but more likely she has turned even more fully to living a Christian life of offering help to those who society sets low in its hierarchy. Realizing that she will not find love again after the death of Dimmesdale and in the wake of so much notoriety, she decides to turn her sunshine upon those who most need it. After all, she now has a new lease on life, with the opportunity to live outside the stringency of society; she can continue to seek peace sincerely, in and from her own heart. She dies alone, but we sense that she has lived a full life, able to ascend to heaven knowing that she has fulfilled not only her duties, but also her love, ensuring that her daughter will continue her legacy of love, truth, and honor.