To show possession, like the necklace’s clasp, the rule is generally to add an ’s to the end of the word that has possession. However, the exception to the rule is the word it. When you add an ’s to it, it creates a contraction (it is) but does not show possession. So the sentence should be “Sasha, who wore a silver necklace every day, said her necklace was broken because its clasp would no longer close.” The commas around the clause who wore a silver necklace every day are appropriate as it is non-essential information that is not critical to understand the sentence.