"It imparted to the wearer a kind of sacredness, which enabled her to walk securely amid all peril. Had she fallen among thieves, it would have kept her safe. It was reported, and believed by many, that an Indian had drawn his arrow against the badge, and that the missile struck, it and fell harmless to the ground." - Nathaniel Hawthorne, The Scarlet Letter - Chapter 13
Wow…this is certainly interesting… It's almost as if the "A" suddenly has been given a supernatural quality. With the people of the town now beginning to almost worship Hester due to her ability to remain strong with her punishment, the letter has been given the meaning "Abel," now obviously spelled "able."
The letter is somehow able to protect her from all harm, out of thin air? Something isn't right about this. Why is it that a sin suddenly has the power to create an invisible force field that protects the sinner? After all of the torture that Hester has undergone due to her supposed penance, wouldn't it seem more natural for this letter to serve as a bad omen to her health? Taking a look a bit before that passage, Hester is even described as losing her feminine touch and looking less than her best.

It is almost as if the author is eluding to the fact that Hester may be gaining superior support, almost a supernatural protection, in light of Chillingworth's cruel tactics toward Dimmsdale and Hester.
This quote stood out to me as well. I found myself asking the same questions... how could a letter protect her from harm?... how could something with such negative intentions protect her? It is clear at this point in the novel that the scarlet letter had specific intentions but it seems to be doing almost the opposite of what was intended of it. Because of this, the powers of the letter are unpredictable.