I'll first say that if the Professor needed a copy of the graded assignments, she could have and should have just made the copy when grading, and kept it. This sounds like an arbitrary "trap" for people who are a little absent-minded, or mere arbitrariness.
First order of business IMHO is talking to the Professor, preferably out-of-class. Explain that you have not kept copies of all your work, and that you were not aware (regardless of who is to blame for it) that you had to do so - and you would like to ask for an alternative w.r.t. grading.
Considering what you've said, this is likely to fail. While waiting for the above meeting to occur, also talk to: 1. Your fellow students in this class. 2. Your student union representative (assuming you have one; otherwise - higher-ups in the student union). If they are willing, consider planning for some sort of collective action or intervention which would force the Professor's hand in case she doesn't agree to flex her positions. It's much easier to avert inappropriate grading before rather than after the fact. What could such an action be:
- Most or all students simply fail to bring any graded assignments as requested. They collectively agree to say they haven't kept copies of them. The Professor would not be able to just fail the whole class (or rather - is unlikely to do so and would be unable to defend the action) and would likely cave either at that point or earlier.
- Student union starts some sort of publicity campaign against this Professor's policy.
- Student union petitions for disciplinary procedures against the Professor (in some universities there's a legal right to start such formal procedures; in some you have to beg).
It's not that I think that these things should be done, but they are not impossible nor inconceivable and should be made possible as fallback in case things turn sour. Regardless of whether such action is agreed upon and readied for execution, either a student union rep or a group of students, and even better - both, approach the Professor collectively to try to change her mind.
But let's parallelize some more. Next step up after the personal meeting with the Professor is the Professor-in-charge for the course (in case it's a different person); then, next up - the person in charge of (undergraduate?) studies in your department. Again, student union rep + many students is the best combination from your side to meet with people further up the chain of authority.
PS - @Buzz's answer also makes some good points - especially about not saying which assignments you have or don't have.