This could be a problem in any class. For all you know, every single essay assigned throughout an entire semester could be written by the student's friend, boyfriend, sibling, etc. It's really difficult to prove and, in some cases, detect this type of behavior.
Detecting and proving cheating can indeed be difficult, but preventing cheating can be quite simple. The following web page will help you design your course to do so:
http://www.learningfield.org/cheat/Also, the fact that the institution does not provide proctoring services doesn't mean that the students cannot use the services of another institution. I arrange proctored exams (ID required!) with students all over the world.
-Erik Jensen
Chemeketa Community College