In chapter XXIII of The Scarlet Letter we find that, after Dimmesdale's death at the scaffold, Pearl seems to somehow transform
Pearl kissed his lips. A spell was broken. The great scene of grief, in which the wild infant bore a part, had developed all her sympathies; and as her tears fell upon her father's cheek, they were the pledge that she would grow up amid human joy and sorrow, nor for ever do battle with the world, but be a woman in it.
Now we know that Pearl's original role as a punisher in Hester's life seem to have changed now that Dimmesdale finally completes the circle of redemption, and exempts her from being just a bastard child of sin and crime. Now, Pearl is the daughter of Hester Prynne and Reverend Dimmesdale.
We also know in chapter XXIV, that Chillingworth dies only within a year of Dimmesdale's and leaves his estate to Hester and Pearl. Now the women are finally free, and they both parted for Europe. We know that their relationship improved, and that Pearl did end up taking care of Hester, even after the latter returned to New England, to the same isolated shack, and to wearing the scarlet letter.
But, through the remainder of Hester's life, there were indications that the recluse of the scarlet letter was the object of love and interest with some inhabitant of another land. Letters came, with armorial seals upon them, though of bearings unknown to English heraldry. In the cottage there were articles of comfort and luxury, such as Hester never cared to use, but which only wealth could have purchased, and affection have imagined for her. There were trifles, too, little ornaments, beautiful tokens of a continual remembrance, that must have been wrought by delicate fingers, at the impulse of a fond heart.