Entirely broken JSON, no — I would be surprised if one existed. If you want slightly laxer semantics like trailing commas, JSON5 [1] is a pretty good spec and is JSON-compatible. I used to use it for LLMs (while telling them to emit JSON — no need to confuse them by explaining JSON5), in order to handle things like trailing commas, but in my experience LLMs have gotten good enough over the last year I mostly don't even bother anymore.

1: https://json5.org/

Should be easy to build on top of a lexer as a pre-parsing pass.

Dirtyjson

You can force LLMs to generate valid json by using a context free grammar FWIW

Please elaborate

Matt Rickard has a good entry level blog post about it, from the angle of regex constraining [0]. Context free grammars follow the same principle, except using a finite state machine to restrict the action space.

[0]: https://matt-rickard.com/rellm

Look at llama.cpp grammars, lmql, or guidance-ai