Plagiarism is a growing problem in creative writing. I advise that all teachers put on their syllabus an anti-plagiarism statement so they will be prepared when the problem comes up.
I had a student steal a short story from an internet magazine from the middle east written in English. That was easy enough to catch on turnitin.com, although the student vehemently denied it until I put his story and the copy I'd printed off from the internet on the desk in front of his face.
Requiring the submission of rough drafts, and requiring the students to write autobiographically, are two ways to help prevent plagiarism.
THE NEW PLAGIARISM is the stealing of plots from films and from TV shows. Often plot summaries are taken from internet. Wikipedia has them, for instance.
Stealing plots cannot be detected by turnitin.com. Also, there are certain motifs in fiction. If a short story in the Western genre has a faceoff, shootout scene, one can't call that plagiarism. That plot point happens in a lot of Westerns. Only a human can determine if enough of a plot has been stolen to call it plagiarism. One must remember also that Shakespeare borrowed plots.
I see a marked decline in reading amongst my students. Writing a short story, even if we read a lot of short stories, continues to mean to them an immitation of a TV show or a movie. It is plot summaries from these genres that they examine for plots to steal.
This is why I am going to stress, in my beginning creative writing course, WRITING FROM AN AUTOBIOGRAPHICAL BASE. I realize the problems inherent in such writing, but it seems to me the most efficient way of preventing plagiarism.