Madame Loisel is the protagonist in Guy de Maupassant's short story "The Necklace". The story is about a woman who longs for a life of luxury and extravagance, but is stuck in a reality of mediocrity. In an attempt to fit in with the upper-class at a fancy ball, she borrows a diamond necklace from her friend, but loses it during the event.
Throughout the story, it is not explicitly stated where Madame Loisel lost the necklace, but there are several indications and events that suggest where it likely happened. Firstly, the necklace is lost on the night of the ball, which was held at the Ministry of Education. The ball was a grand event attended by the wealthy and influential, and was therefore a high-pressure situation for Madame Loisel, who was already anxious about fitting in.
Furthermore, it is noted that the night was very busy and chaotic, with many guests milling about, music playing, and champagne flowing freely. In such a frenzied environment, it is not surprising that Madame Loisel would have become flustered and careless, and perhaps dropped the necklace without noticing. Additionally, she and her husband frantically search the entire ballroom and surrounding areas, but are unable to find the necklace, suggesting that it may have fallen somewhere in the crowd and been accidentally stepped on or otherwise lost.
In conclusion, based on the events of the night and the circumstances surrounding Madame Loisel, it is likely that she lost the necklace at the ball, most probably in the busy and chaotic environment among the guests. Her anxiety and carelessness, combined with the hectic atmosphere, would have created the perfect storm for the necklace to go missing.