Farquhar wasn't executed.
Answer
One of the central themes of "The Necklace" is that of appearance vs. reality. For Mathilde, the necklace symbolizes wealth, beauty, and, ultimately, shame, as she loses the necklace and goes into debt to replace it. The great irony of the story is that the necklace was a fake. Mathilde spends ten years in debt, effectively ruining her life over nothing.