To properly answer this question about the short story "The Shed Chamber" by Laura E. Richards, it is important to trace some of the story's background. Nora, the narrator, is a young teenager who answers an advertisement for "a capable, steady girl to assist in housework and take care of children." She travels to the home of Mr. and Mrs. Bowles and their two children. Mr. Bowles is a businessman and Mrs. Bowles is an invalid. Nora quickly becomes indispensable in minding the children and cleaning up.
One of the first things that Nora discovers is that the kitchen is "in a scandalous condition." The previous girl had been inexperienced and inept and had left it in a mess. Later we find out that Annie is the girl that Mr. Bowles had hired before Nora, so she is responsible for its mess and disorganization.
Nora does so well looking after Mrs. Bowles and the children that Mr. Bowles feels confident enough to go off on a business trip. After he is gone, however, Annie appears at the door at night and asks to come in. When she thinks she is alone in the shed chamber, she lets in a thief with an "evil, coarse face" and hides him in a cedar chest. Nora is able to help thwart the robbery and capture the thief by running for help.
Richards does not clarify the motivation that causes Annie to assist the thief. She leaves it up to readers to figure out. The clue to this, and to the earlier mess in the kitchen, and also to the reason why Nora does not turn Annie in, is in the last paragraph. She writes,
She was just my own age and she had no mother.
Nora has a mother who she can talk things over with and who is anxious for her when she is gone. Nora empathizes with Annie. She probably doesn't know what she would do if she lost her own mother, but if she puts herself in Annie's situation, she can understand her loneliness and desperation. It has also been made clear earlier in the story that Nora has a kind and helpful heart. Instead of telling on Annie and coming down hard on her, she goes to visit her so that she can understand her. In becoming Annie's friend, she somewhat mitigates the unbearable loss of her mother.