In chapter four, when Hester is suspicious that her husband Chillingworth might take revenge on her for her affair, Hester tells Chillingworth, "I have thought of death... have wished for it, - would even have prayed for it, were it fit that such as I should pray for any thing." Chillingworth follows this statement by saying, "Even if I imagine a scheme of vengeance, what could I do better for my object than to let thee live... so that this burning shame may still blaze upon thy bosom?"
Later, in chapter seventeen, Hester has to decide if she will reveal her relationship with Chillingworth to Dimmsdale. "Hester felt that the sacrifice of the clergyman's good name, and death itself, as she had already told Roger Chillingworth, would have been infinitely preferable to the alternative which she had taken upon herself to choose. And now, rather than have had this grievous wrong to confess, she would gladly have lain down on the forest-leaves, and died there, at Arthur Dimmsdale's feet." Hester chose a life of public shame, a life of an outcast, as an act of penance for her sin. It would have been easier and preferrable to her to simply be killed for her crime and be done with it.
Question is not quite clear.,hester is shown as a victim of puritan society. She is brave and courageous as shown by Hawthorne. She has opted right path to live in the same town where she was humiliated. So she has preferred life of troubles or life of severe sufferings which can purify her guilty soul.