Roger does not run because he is intrigued by Mrs. Jones and she is being supportive of him.
When Roger tries to snatch Mrs. Jones’s purse, she does not scream or call the police. She knocks him down, grabs him, and takes him home. Once home, she basically takes care of him.
At first, Mrs. Jones still has Roger “by the neck,” so he isn’t going anywhere. She asks him his name, and tells him to wash his hands. He decides to do it.
"Then, Roger, you go to that sink and wash your face," said the woman, whereupon she turned him loose--at last. Roger looked at the door—looked at the woman—looked at the door—and went to the sink.
Roger asks if she is going to take him to jail, but he stayed, so he either doesn’t believe it or is willing to just go along with her. He trusts her and respects her. He is not a bad kid, but he has made a bad choice.
As the evening goes on, Roger learns that Mrs. Jones does care about him. She wouldn’t have brought him home if she didn’t. She will make him a meal and tell him about her life, and even ask him why he tried to steal from her. What an unusual occurrence!
Mrs. Jones opens up to Roger, and confides in him.
The woman was sitting on the day-bed. After a while she said, "I were young once and I wanted things I could not get."
This reveals the reason she brought him home, instead of calling the police on him. She saw something of herself in him.
Maybe Roger will change, and maybe he won’t. One thing is for sure—he has had a unique experience. He has learned that he is not completely alone in the world, but he has also learned that life is not about just taking what you want. Roger may not have made the right choice in trying to steal the purse, but he made the right choice in going to the sink—in staying instead of running.