There is definitely a theme regarding the need for possessions in "the Necklace." The young woman in the story, Mathilde, has a comfortable life, but does not have the materials possessions (fancy clothes, servants, etc.) she wishes she had. So she is ashamed of her life. It eats away at her. She cannot see "It's not having what you want, it's wanting what you've got."
When Mathilde and her husband are invited to a ball, Mathilde laments over having no jewelry, but there is no money for it: her husband works hard as a clerk, though he does buy her a new dress.
So Mathilde goes to a friend (Madame Forestier) and asks if she may borrow some of her jewels. Her friend readily agrees, and Mathilde goes to the party feeling complete, wearing a "diamond" necklace. Having the jewelry about her neck makes her feel special and complete.
When she loses the necklace, Mathilde and her husband go into great debt to replace the jewels. They have to do without; Mathilde has to work and can no longer enjoy the life of comfort she once knew. She works herself into the ground, worries and scrimps, and she ages physically beyond her young years.
At a later date, running into Madame Forestier, Mathilde speaks about the necklace and relates what she had never revealed before: that she had lost the jewels. Her friend is dismayed: they were not real. Mathilde and her husband have lost years of joy and comfort paying for gems made of paste, all because Mathilde believed that material possessions would make her happy.
When one considers the difference between a subject and theme, a theme is a universal truth expressed as a sentence while a subject is an idea that the story is about such as greed, lust, fame, material wealth, etc. "The Necklace" is an apt title as it is the "McGuffinn--(from Roger Ebert of the Chicago Sun Times)--an object which merely moves the story along. It does play a prominent role, however. Though Mathilda never asks about the necklace nor admit to losing it, there seems to be something else at work besides material wealth or the desire for material wealth. For de Maupassant, that would be too easy. The story, if one looks closer is about our expectations and our perceived expectations of what we should be entitled to. It ha s a more psychological aspect than simple greed, and makes the character of Mathilda that much more real. The fact that she ends up working for years to pay off the price of what she perceives as the value of the necklace in which ti turns out the real value is small, one understands that de Maupassant was after something much more valuable to say about people's perception of who they are and who they think versus who they really are.