When employed as slang for hanging suicide, the term "back to school necklace" is actually a euphemism for a noose, according to a fast Google search. According to Urban Dictionary, who keeps track of the definitions of slang terms, the following definition and example sentence:
"A noose is also known as a back-to-school necklace. This is a result of the complete dejection you experience when classes resume. Yesterd
ay was the first day of school, and I finally gave up and got a back-to-school necklace.