Usage-based theories of grammar explain language users' ability to interpret and produce novel combinations of words through two complementary inferential strategies. In cases of coercion, a language user, when encountering a word that is mismatched to its grammatical context, reinterprets that word in a way that resolves the conflict. In cases of preemption, the user infers that an otherwise plausible structure is unavailable or dispreferred because it fails to occur in contexts where it would be expected. Large Language Models are also usage-based, in the sense that the structures of language are learned through exposure to vast amounts of text. Here, we test whether or not the opposing forces of coercion and preemption also encourage and constrain linguistic productivity in LLMs. We demonstrate across models of various sizes and architectures that larger models recognize constructional productivity in cases of coercion, even when these involve novel words. However, we also show that even the largest models do not replicate the conservative language strategy of preemption for novel words: in particular, they do not appear to draw on negative evidence when making choices among competing grammatical options. We conclude that coercion is detectable because it is both surprising and semantically motivated: when a word is mismatched to its syntactic context, the word's meaning can be adjusted to fit the context. Preemption has no such signature. There is no record of the lexeme-construction pairings that were avoided--only of those that were produced. This asymmetry helps to explain why models coerce (create mismatched sign combinations) but do not preempt (avoid unconventional yet semantically defensible ones).

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