Society can't fix everything

As seen in almost every novel we've read this year, there is always some entity that is shunned or ousted by society for challenging what was deemed as rectitude or acceptable.  In The Scarlet Letter, Hester challenges what was deemed conventional by demoralizing the meaning of her "marriage"with Chillingworth.  She decides to cheat on him thinking that the relationship she possessed with Dimmesdale and what they had done was consecrated.  She eventually is able to turn this horrible and atrocious life-long reminding "A" into a symbol that represented a bigger picture of repentance and general goodness.  In almost all of the books we've read this year, society has tried to fix this misfits, but I personally feel that they are never going to be able to succeed converting this "mishaps" into what is socially acceptable.  So I was wondering, just to spark some friendly debate, does society eventually "fix" Hester by branding her this adultery-committing sinner, or does she instead internalize this symbol, make it her own, and transform the meaning of it entirely and in essence, "own it."  Feel free to  comment your ideas and the more evidence, the better.

Salvatore