Take the verb 座る. As a punctual verb, it appears as 座っている when describing a person who "has sat down and remains sitting." When using the negative, there are two options: 座らない and 座っていない.
Given the question, "Is Tom the guy who is seated?" and the response "Tom is not sitting, he's the guy doing jumping jacks", which form of the negative matches the intended meaning? What would the other form mean?
This question was prompted by learning that the appropriate negative of 知っている is 知らない, and none of my learning resources describe anything about 〜ている forms in the negative.