The LLM doesn't "know" anything, can't reason about its own knowledge, and has no self-awareness. It has training data, and it can use your prompts to synthesize that training data into probable continuations or responses.

If the training data doesn't include lots of text of people being asked questions and saying "I don't know", then it's unlikely to respond "I don't know" when prompted, regardless of whether anything in its training data that might actually answer your question.