The worst grade I got during school was that one time I was sick, told the teacher and she just sent me to the library to do the exam there, because it would be quieter there... failed that test horribly. Only got like 1/4th of the points and couldn't do anything about it. No second chance, nothing.
In Uni, you would always be asked if you are well enough to write the exam. If you felt sick, you had to say it before the exam and I think you just had to take the next exam available (you had two chances per semester). You got to skip the exam, basically. You most likely had to go to a doctor afterward and get a doctor's certificate (sick leave), otherwise people would have abused it a lot.