Imagine we have some sort of "next token predictor," either with transformer architecture, LSTM, or just a HMM (though the terminology I use here will be less aligned to HMMs, I believe the question is generalizable to all generative NLP).
We reverse the cost function. That is, we are training to maximize error instead of minimizing it. In the case where error is neither maximized nor minimized, the behavior will be fairly boring. However, a model which is maximizing error may still need to learn patterns of syntax and which words usually follow one another in order to avoid them. I would expect that in some abstract way, it may behave creatively, because it is trying to produce output which is not in the training data, and is furthest away from it. In fact, it ideally should understand the user's query in order to avoid using words that follow it.
This makes me think the output may be non-boring, although probably not practically useful.