Something so many people seem to forget is that teachers are humans too.
If you will just communicate with them, almost every single teacher I have ever had is willing to break their "no exceptions" policy.
One example, last year in my English class, I managed to pull out a B average grade. I did probably D work. I turned in almost nothing on time and it was nothing close to the best I could do.
My life was also beginning to fall completely apart. Things with school, money, family, friends, I was just trying to stay afloat. I would go to turn in my partial work on time and apologize. I would say "I expect no special treatment, it's not finished, but here is what I do have." Almost every time my teacher would say "Just bring it to me when you are done."
It probably helped that we had journals in that class and a lot of my writing would contain everything that was falling apart around me. So she knew I wasn't just making it up. That, and several people said that I looked like I hadn't smiled in a long time.
I figured she would probably give me a C-, enough to pass me, but really still generous for the work I was doing. Nope, averaged a B. (I don't remember if it was + or -, I just remember the B part.)
I have had several other occasions where teachers have been angels of mercy simply because I communicated my problems to them.
I think that is what we sometimes forget as students, our teachers are these huge scary giants that rule with iron fists. They are human beings. They have to set strict guidelines because so many students will push the limits around, it's just how we tend to work. They also know that "No exceptions" means "No exceptions that will apply to the entire class, but if something extraneous happens, come talk to me and I'm sure we can work something out."
Today, I am just grateful and happy that teachers are human beings.