The Broken Necklace is at the path of the Fields that lead to the Hills. It is right after the broken bridge that was patched up with a Soft Wood Board. It is automatically picked up as soon as its seen.
The Broken Necklace belongs to the Woman in the Rice Fields when she was still alive. Losing it before she died was part of the reason her spirit refuses to move on and become a restless and resentful spirit trying to get back her necklace no matter the cost, even go as far as killing people. By returning the necklace to her corpse at the bottom of the Cliff, the Spirit will be appeased and stop trying to kill the Protagonist.