An example from an earlier comment of mine on a different thread (assuming I've understood correctly):

> let's say we had a grammar that had a key "healthy" with values "very_unhealthy" or "moderately_healthy." For broccoli, the LLM might intend to say "very_healthy" and choose "very" but then be pigeonholed into saying "very_unhealthy" because it's the only valid completion according to the grammar.

That said, you can use beam search to more or less solve this problem by evaluating the joint probability of all tokens in each branch of the grammar and picking the one with the highest probability (you might need some more nuance for free-form strings where the LLM can do whatever it wants and be "valid").