Here's what happens:
* Billy and Stuart are revealed to be the killers. They are working together to terrorize Sidney and her friends.
* Stuart is injured during a struggle with Randy Meeks. Randy accidentally shoots Stuart in the leg with a shotgun.
* Billy tries to escape with Sidney. He takes her hostage and they are confronted by the police.
* In a final confrontation, Sidney grabs Billy's gun. Billy, believing Sidney is about to shoot him, begs her not to.
* Sidney shoots Billy. She does this in self-defense after he attacks her.
* Stuart is left alone and vulnerable. He is then killed by Sheriff Dewey Riley, who arrives on the scene.
So, while Sidney doesn't directly kill Stuart, she plays a crucial role in his demise by shooting Billy, which allows Dewey to take him down.