As a college professor, one thing I've learned is that I need clearly stated policies regarding every aspect of my classes. This applies to grades, especially. My policy, I think, is simple. Any assignment past due by three days receives an automatic zero. Students can contact me for permission to turn in late work, but that doesn't mean I have to grade it. I also tell students in my syllabus that they need to remind me--before dead week--of any assignments they submitted that I agreed to grade.
I have a freshman from last semester who contacted me after final exams about her grade. I have been going back and forth with her--though, again, my syllabus says that I will not discuss grades when dead week begins. I have reminded her of my policies, but she persists. Perhaps she thinks that "the squeaky wheel gets the grease"--that if she bugs me enough, I will relent.
What generally happens is this--I go to the chair of my department and the dean of the college and explain what's going on. My policies are clear. I remind students about them constantly, especially at the end of the semester. Students must submit all assignments to keep from making an automatic F in the class. That still doesn't mean I'll grade the late assignment.
I have to jump through hoops to change a final grade in a class. That's why it's important for students to read and understand my policies. If I make one exception, then any student who didn't submit work and wants to do so now can use this one case as justification. I like to be consistent.
I don't know how this will resolve, but it's something that won't go away until I hand it over to my bosses. I hate dealing with this kind of stuff. It detracts from the work I need to do now.