We are never told what happens to the lost necklace in "The Necklace." All we know is that Madame Loisel loses it at the ball, and she does not even know at what point she loses the necklace, only that it is gone when she and her husband are getting ready to leave. We can speculate. Someone might have found it, believed it to be a real diamond necklace, and kept it or sold it. Someone might have found it and attempted to find its owner, to no avail. The cleaning people might have picked it up after the ball and thrown it away.
What is important about the lost necklace is its symbolism. The necklace is lost in the same way that Madame Loisel's hopes and dreams for upward mobility are lost, condemning her to years of hard work and debt. For some, the story's meaning is that she is being punished for her aspirations, but really, this seems to be a punishment for her dishonesty, in her trying to represent herself as something she is not, and even more importantly, in her dishonesty with her friend, whom she does not immediately tell of the loss of the necklace.
It has occurred to me that some unscrupulous man might have stolen the necklace right from around Mathilde's neck. There must have been jewel thieves who obtained access to social gatherings such as the one in the story. The necklace would be a tempting target. And Mathilde Loisel would be an easy victim because she was not used to wearing such jewelry. A skillful thief could unfasten the clasp with his fingers and slip off the necklace as he whirled the young woman around on the dance floor. Imagine that thief's chagrin when he tried to sell it and found that it was a cheap imitation!
The most famous jewel thief in literature is A. J. Raffles. His creator E. W. Hornung wrote twenty-six stories and one novel about this "gentleman-thief." Raffles would never steal a fake diamond necklace.
Of course, I am just speculating that the necklace might have been stolen. Maupassant seems to want to create the impression that it came off while Mathilde was hastily putting on her "wraps" in order to escape from the house before the other women could see that her outer clothes were of poor quality. She seems a bit like Cinderella in the fairy tale who lost one of her glass slippers in her haste to get home before midnight. Maupassant may have been thinking of that fairy tale when he wrote "The Necklace." Like Mathilde, Cinderella was a beautiful girl who never got to go anywhere.