Using the literary meaning of the word salvation,
a. Preservation or deliverance from destruction, difficulty, or evil.
b. A source, means, or cause of such preservation or deliverance.
it is then safe to assume that, in the case of Roger Chillingworth
, his salvation correlates to any opportunity or event that would have helped him to move away from the constant cycle of anger, revenge, and spite that was, literally, eating away his body and soul. His anger, which stems from feeling cuckolded by Hester
, and his sense of revenge against Dimmesdale has brought upon Chillingworth a perennial evil atmosphere
that is detectable even in his appearance. So abrasive is his presence that even the townspeople begin to suspect something almost weird and otherworldly in him. No longer can he ever attempt to look like an older, and philosophical physician. His anger has transformed him dramatically
(he) had altogether vanished, and been succeeded by a eager, searching, almost fierce, yet carefully guarded look.
That Chillingworth would
mask this expression with a smile, but the latter played him false, and flickered over his visage so derisively that the spectator could see his blackness all the better for it.
Shortly after Dimmesdale's death, however, Chillingworth realizes that he has basically dedicated his entire elder existence to the destruction of another man. All the essence of his soul sort of dies with Dimmesdale and Chillingworth realizes that, like his rival, his own life will come to an end quite soon.
Hence, his salvation is defined by the moment when he really looks back and chooses to transform his actions to that he can be moved away from evil. The way that he does this is by leaving all of his riches and possessions to the most unlikely character: the very child born from the indiscreet relationship between Hester and Arthur Dimmesdale
So Pearl--the elf-child,--the demon offspring, as some people, up to that epoch, persisted in considering her--became the richest heiress of her day, in the New World.
This completes the circle: Pearl's new status allows her to take care of Hester who, in turn, can also benefit from her daughter's social respectability. In all, Roger Chillingworth's leaving his fortune to Pearl is a way of paying back for all the pain and suffering that he may have caused Hester. Giving support for Pearl may have been his way of blessing and forgiving the adultery between Hester and Dimmesdale. However, there is always room to wonder whether Chillingworth's own guilt and fear of going to Hades on his death bed are behind his motivations to be kind.