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Btw. I know nothing about Abessive Case, but "Я не строю трагедии из произошедшего" and "Я не сделаю упражнения к завтрашнему дню" sound incorrect for me anyway (if we talk about the singular forms...

Well, may be those examples and their assessment aren't very good. But what i would say was about substitution accusative case for genitive (deliberately or by mistake). It sometimes occurs. I know...

Actually, it fairly often happens when we substitute accusative case for genitive in colloquial speech, and contrariwise.
E.g. 1) "Я хочу (попить) воду"(incorrect) и "Я хочу (попить) воды"...