The borrowed necklace is the same as Madame Loisel’s dreams because both are artificial and seem to be something they are not.
Madame Loisel wants to be more than she is. She considers herself a high society woman, but in fact she is the husband of a clerk.
The girl was one of those pretty and charming young creatures who sometimes are born, as if by a slip of fate, into a family of clerks.
When her husband gives her an invitation to a ball, he expects her to be excited. Instead she is angry, because she has nothing to wear. She will stand out in a clerk’s wife’s clothes. He gives her money to buy a new dress, and suggests that she borrow a jewel from her wealthy friend.
Mathilde borrows the jewel, and loses it. She borrows money to replace it, and spends a very long time working to earn the money back. She loses her beauty and youth. When she sees her friend again, she is shocked to learn that the jewel was fake.
Like Madame Loisel's dreams, the fake necklace is not what it seems. She is not what she seems. She is not really the high society woman she thinks she is. She loses her real self in the quest for her fake self.