They do invent code solution for the problem that exists in your codebase. Latter implies that the code solution LLM synthesizes is usually unique of a kind, so, it's not a copy-paste neither it is a simple extract from "another codebase" and adopted.

IMO they operate pretty similarly to humans - we synthesize our solutions, and therefore build-up our knowledge, by collecting knowledge from multiple other sources, including technical books and blogs, open-source code repositories, and our past experiences.