Is it fair for a professor to grade us on the possession of past papers? My English professor recently asked us to bring in all of our graded essays from the whole semester in order to fill out a 'rubric' of sorts which tallied the various types of mistakes we had made. She will be grading the rubric, and previously stated that if we did not have all the essays from the past semester in class that day, our grade would be comparably lower than otherwise. She made no mention of 'keeping all graded work' at any point during the course, and in my current institution, I have never been expected to keep past work for any specified duration. There are a multitude of reasons why a student may not have been able to keep particular (or any) essays, which my professor did not take into consideration. 

Is it fair for my English professor to expect us to keep all of our past graded work, and then grade us on our possession? If unfair, how can I bring this issue up with her and dispute her expectation?

Note that I doubt that this is because she lost the essays; they’ve already been averaged into our final grades.
If this was not mentioned in the syllabus (or at least announced prior to the papers being returned), this is totally inappropriate.  While it may be foolish for students not to keep their graded work (at least until the end of the term), if it was not established as a requirement before the students got their papers back, it cannot reasonably be made a retroactive requirement.

You should bring this problem to the attention of the instructor.  You do not need to reveal whether you actually have all your past papers when you bring this up, lest the instructor try to wave your concerns away if you say that you actually do have all the papers and are just complaining as a matter of principle.  I would also suggest having multiple students come to her together to make the same objection; that may make it more likely that she will relent.  However, if the instructor does not agree to make a change, you should take this up with someone higher up.  That could mean the department chair (or another departmental official, such as the director of undergraduate or graduate studies) or a student ombudsman, if one is available.