If that occurs and it’s a substantial enough body of output that it is itself copyrightable and not covered by fair use. Confluence of those conditions is intentionally rare.
If the LLM reproduces a human's copyrighted work, then that copyright still stands. This is, in effect, the same as photocopying someone else's writing. The LLM was trained on the copyrighted work, is incapable of producing new copyrightable work, so if it duplicates the original work then the original author's copyright still stands.