Any change to the grading scheme of a class should be Max(old grade, new grade). One of my profs once offered a re-test opportunity such that you would have had an incentive to do worse on the exam for certain original scores. Drove me up the wall.
> ... I ended up ... neither a zero-day ...
> Realizing everyone in the class would fail, the professor changed the grade of this project to only account for 30% of the grade.
> I ... disregarding the rest of the busy work for the class.
It sounds like OP could not find a zero day (old_grade=0) and did not do any other homework (new_grade=0), therefore should have received max(0, 0), but received a C.