What are some tips for adding an installment to the novel which expands and develops upon a social, moral, or ethical issue from the perspective of a secondary character?

This assignment sounds like an interesting one, and you can develop ideas for your short story inspired by The Outsiders in a number of different ways. Here are two ideas to get you started.
First of all, which of the characters in The Outsiders resonate with you the most? If you felt a connection to the conflicted and complicated character of Cherry Valance, you might imagine her reaction to the death of Johnny Cade in a more thorough way. What if she was asked to write a letter to Johnny as a way to reconcile her feelings about his death and his murder of Bob? Your short story could take the form of this letter, and you could focus your narrative on Cherry's emotional and internal world, as well as her own grappling with the ethical considerations of what happened.
Another interesting short story could be written from the point of view of Sodapop as he interacts with a social worker who comes to interview the Curtis brothers. What does this social worker see, and is it enough to allow the boys to stay together? Make sure you include dialogue and spoken words from each of the Curtis boys that imitates their manners of speaking in the novel.