"posiłak" is not a word, but I will assume that this was just a typo. But no, "Kobieta nie je posiłek" is not a correct sentence.
So basically, "jeść" (to eat) takes Accusative, which here is "posiłek". But it's negated. When a sentence using Accusative is negated, it takes Genitive instead. "posiłek" turns into "posiłku".
That is the only situation when negating the sentence changes the case. Other cases stay the same.