fwiw it doesn't/that was a joke. In some cases the LLM will suggest running a command that doesn't terminate (eg npm run dev to run a webserver), so it'd get stuck running that command just waiting for user input.
You jest, but given something that's in it's training data, ChatGPT's able to say the code won't terminate (eg a code to give all the Fibonacci numbers), so there are subsets of the halting problem it can solve for.