Let us remember that the necklace in Chapter One is explicitly identified as a symbol of allowing new experiences to enter our lives, just as the catch on the necklace opens spontaneously to let new things enter. Therefore, the way in which the necklace passes through the hands of so many characters is symbolic of the way in which the characters learn to embrace new experiences and also the way that the lives of the various people "criss cross," as the title of this work suggests.
It can be quite hard to keep track of the many different characters who find the necklace before it passes on again, but here are the main events relating to the necklace and its ownership. In Chapter 16, Russell finds it when he is taking out the trash. In Chapter 17, Hector finds it while at the Tastee-Freez. In Chapter 19, Dan was looking for it, but from his pocket it had fallen onto the trunk lid of Rowanne's car and then onto the street. In Chapter 36, Hector finds the necklace on the street as he goes to the luau in his Hawaiian outfit. Lastly, in Chapter 38, Hector gives it back to Debbie which seems to symbolise the potential they have to form a relationship.