I agree that Juliet cuffed herself to Kate. She knew Kate would have nothing to do with her and would not work with her, or help her, or take her to the beach. Now, I am not sure if she did this because she truly was left behind and was trying to ensure her own survival, or if she was only left as a plant and this was only a tool of manipulation. There is one other possibility. Ben had them cuffed together and slipped the key in Juliet's pocket in order to set up a situation of mistrust.

I am leaning towards Juliet being a spy right now. The whole set up with Jack feeling as though he saved her from execution......this is a powerful tool to getting her embedded in the group. He will be all protective of her, and insistent that she be accepted by everyone.
Otherwise they would have had no hope of her getting in at all.