The way it works is to disallow invalid next states, and getting backed into a corner is one way to think about one possible failure mode.

For a concrete example (happens less nowadays with bigger models, but it still happens, especially later into a context window), models hate long json strings. It's very easy to get a json output like

{"name": "Bob", "biography": "Bob is a fantastic builder, having ...

Critically, the ellipses terminate the JSON. With schema-constrained decoding, you _must_ eventually terminate that broken string, and it'll typically terminate it right after the ellipses. Basically, by the point you got to the first period the output was borked. You were backed into a corner. Retry as a strategy fixes that.

As another example failure mode that's a bit more subtle, you might have a set of "correct" tokens early on in the output which get the KV cache into a bit of a wonky state, causing it to have worse outputs toward the end of your output. Disallowing invalid next states forces you to generate tokens in that worse-output state. Retry lets you fail more often and then hopefully not have those wonky-state early tokens. It's not really that you were backed into a bad state as a hard rule, but that you were backed into a bad state as a probabilistic statement.

For a toy model to think about, suppose the entire grammar is [ab, ba], and the LLM's universe of training data is [ab, ab, ba, bb]. The "right" distribution (retry on failure) is {ab: 67%, ba: 33%}. The schema-constrained distribution is {ab: 50%, ba: 50%}.