Mrs. Luella Bates Washington Jones is not a wealthy lady when it comes to her finances, but she does have a wealth of character. She's willing to share the little she has with a boy who tries to rob her because she can see past his negative actions to the hopelessness and sorrow beneath them.
It's clear that Mrs. Jones isn't rich when one examines her circumstances. She lives in a house with other roomers. She's walking home alone at night. She has a large, utilitarian purse that breaks with only a pull on the strap. She says that she was young once and wanted things she could not get—showing that she has empathy with the boy's lack of money.
Near the end of the story, she explains that she works in a hotel beauty-shop that stays open late.