Who is to blame for the unfortunate turn of events in the necklace?

The blame arguably lies with Mathilde. She is a vain, shallow woman who thinks that money and worldly goods will bring her happiness. In borrowing money at an exorbitant rate of interest, she directly contributes to the demise in which she becomes the shambling, pathetic figure that Madame Forestier encounters at the end of the story.
Everything Mathilde does is for show, and the fake necklace neatly exposes the falsity of the world she inhabits. It also symbolizes the real world, a world that is mainly mundane and ordinary, far removed from the tinsel glamor of a society gathering. The everyday world stands in contrast to the glittering facade of the deluded fantasy world she has constructed for herself.
Ultimately, Mathilde has failed to come to terms with her relatively lowly origins. In her heart of hearts, she believes herself a princess. In "The Necklace," De Maupassant is quietly drawing attention to the way in which a hierarchical, class-obsessed society distorts our values and makes us strive to be something we are not. The blame for the "unfortunate turn of events" undoubtedly lies with Mathilde, but her foolish actions can best be understood against the background of a society in which wealth and status are everything.