This is the most misunderstood risk. When you submit a paper to a legitimate Turnitin class at your university, your professor generally has the option to not store the paper in the global repository. However, those "free" classes? They are usually configured to store everything.
Questia offers a free plagiarism checker for students. It scans the web and books. It is not as deep as Turnitin, but it will catch copy-pasted web sources. turnitin class id and enrollment key free
A case-sensitive "password" (created by the instructor) that students must enter to join a specific class. This is the most misunderstood risk