In Section 1, Mary Richards laments that her husband, Edward, was not the man who performed the favor that earned the mysterious sack of gold as a reward. As she remarks on the "fortune" that the gold represents for whoever had been kind enough to perform this favor, she makes an idiomatic allusion:
Mrs. Richards sat down, gently quivering with excitement, and was soon lost in thinkings—after this pattern: “What a strange thing it is!...And what a fortune for that kind man who set his bread afloat on the waters!...If it had only been my husband that did it!—for we are so poor, so old and so poor!
To “set bread afloat on the waters" is an idiom that means to do a deed without expectation of a reward. This idiom is itself an allusion to a passage in Ecclesiastes, a section of the Hebrew Bible and the Christian Old Testament traditionally attributed to King Solomon of Israel: “cast thy bread upon the waters: for thou shalt find it after many days.”
Though Twain may or may not have selected such an idiom because of its biblical implications, its inclusion in "The Man That Corrupted Hadleyburg" nonetheless underscores the significance of notions of Christian virtue to the citizens of Hadleyburg (and, more generally, to the many rural communities in America that Twain made the subject of much of his writing). The central, ironic conflict in the story satirizes this sense of morality: each citizen is vain to the point of pretending to have been virtuous enough to have done a good deed.
In Section 3, the stranger (and the many, many other people who have long awaited Hadleyburg's downfall) finally begin to get their revenge on the town for its excruciating sense of superiority and brutal treatment of outsiders: eighteen of the nineteen prominent citizens of Hadleyburg have revealed themselves to be liars and frauds by all concurrently claiming to be the rightful heir to the mysterious sack of gold. The joy of the crowd, witness to this spectacular fall from grace, only grows as Reverend Burgess reveals the claim made by each successive member of the Nineteen. When Burgess reveals Mr. Pinkerton's claim to the bag, only the third to be read, Twain uses an idiomatic expression that comes from Shakespeare's Hamlet to express the crowd's delight:
The pandemonium of delight which turned itself loose was of a sort to make the judicious weep. Those whose withers were unwrung laughed until tears ran down[.]
To have one's "withers" be "unwrung" means to be unaffected or unafflicted. Twain paraphrases the line from Hamlet, Act 3, Scene 2, in which Hamlet declares to Claudius: “Let the galled jade wince, our withers are unwrung.” Literally, the idiom refers to the wear-and-tear on a horse's back: a "galled jade" is a sore, worn out horse, and the "withers" are a part of a horse's back right below the neck. Unlike a sore horse, Hamlet means to say, he feels fine.
Accordingly, in "The Man That Corrupted Hadleyburg," those whose withers are unwrung are those outsiders and townsfolk in the crowd who have been unaffected by the erupting scandal of the false claims to the gold (in other words, everyone in the crowd save the Nineteen)—and they rejoice accordingly.
