What are some good things that Jimmy Valentine did in "A Retrieved Reformation" to not get arrested?
In the first place, Jimmy Valentine opens a shoe business in the town of Elmore, Arkansas, so that he would have a legitimate "front" while he continues to operate as a safe cracker in the vicinity. He falls in love at first sight with Annabel Adams, daughter of the town's leading banker, and decides to go straight in order to be worthy of the girl.
Mr. Ralph Spencer, the phoenix that arose from Jimmy Valentine's ashes—ashes left by the flame of a sudden and alterative attack of love— remained in Elmore, and prospered. He opened a shoe-store and secured a good run of trade.
He writes a letter to a friend offering to give him all his specialized burglar tools and telling him he is giving up crime. The letter includes these words:
Say, Billy, I've quit the old business—a year ago. I've got a nice store. I'm making an honest living, and I'm going to marry the finest girl on earth two weeks from now. It's the only life, Billy—the straight one.
Then when Jimmy happens to be in Annabel's father's bank, a little girl becomes accidentally locked in the new burglar-proof vault and her life is in danger. Jimmy has his suitcase of burglar tools with him because he was going to take them to his friend. He courageously exposes himself to certain arrest by his nemesis Ben Price by opening his suitcase and using his specialized safe-cracking tools to open the vault and free the hysterical little girl. In doing so, Jimmy seems certain to lose his fiancee, to lose his business, to lose his respectable reputation in the community, and to go to prison for a long time, possibly as long as ten years. But Ben Price shows his understanding and appreciation for Jimmy's reformation and noble sacrifice by declining to arrest him. Ben Price pretends not to know Jimmy in his new identity as Ralph Spencer.
“Hello, Ben!” said Jimmy, still with his strange smile. “Got around at last, have you? Well, let's go. I don't know that it makes much difference, now.”
And then Ben Price acted rather strangely.
“Guess you're mistaken, Mr. Spencer,” he said. “Don't believe I recognize you. Your buggy's waiting for you, ain't it?”
So Jimmy Valentine's reformation was, as the title says, "retrieved" because of his change of character and because of his noble act of self-sacrifice in saving the life of the little girl. Ben Price is satisfied that Jimmy will never again commit a crime and that he will be a law-abiding citizen and an asset to his community. The lovely, virtuous Annabel Adams is largely responsible for Jimmy Valentine's reformation and for his escape from arrest and imprisonment.