Laura

Laura gives Jim the unicorn almost as a "thank you." Although their relationship will neve progress, Jim's presence in Laura's life even for a brief time changed her. It made her feel like she belonged. Thus, like the broken unicorn (now considered a horse), she was no linger different from everyone else. 

Laura keeps the menagerie as a means of escape. They provide her with the opportunity to imagine herself somewhere else.... to be a different person.