Handling N/As which are not missing values in a classification model

I am facing a problem of N/As in classification model and haven't found similar problems.

My dataset contains data on scores of students sitting an entrance examination. The exam contains $$8$$ subjects, and each student can sit $$n$$ subjects where $$3 \le n \le 8$$. These $$8$$ subjects are divided into $$5$$ groups, each group containing $$3$$ subjects. The total scores of any groups of subjects will be submitted for the screening.

By some way, someone has been detected correcting scores of some students to help them pass the exam: he raised the scores of 1 or 2 group(s) of subjects, and lower the scores of any subjects outside these groups (so that the average score is not so suspicious).

The data is labelled so that we know which students being corrected scores as well as actual scores of those students. Now I would like to run a classification model to detect fraud (logistic regression/decision tree...) but am facing one problem: how to handle N/As in the model. Because the number of subjects each students taking are different (can be any ranging from 3 to 8), there are many N/As values. I don't think I can treat them as kind of "missing value", because the N/As themselves here can somewhat reflect the way of fraud (for example, some students aim for natural science so they don't sit in so many social science subjects, and the fraud technique is to lower scores in some social science subjects and raising scores in natural science). I cannot treat N/As here as 0 or average values as usual because it does not make sense.

Is there any way to include N/As in the model in this case?