They can say I don't know when they contain the fact that they don't know something. For instance saying "I don't know" could be a response to"What is the meaning of life"
On the other hand if you ask a LLM how to do something about fish maintenance that it does not know how to do, it might produce an answer like "Sure, first take your fish and " at which point all of the options for the next word are all over the place because there isn't the information available to guide the choice. The sentence started as if it knew the answer because there was no information to say that it didn't. By the time the absence of information has an impact, the LLM is already committed to the sentence where it is confidently giving you an answer.
On the other hand if you ask a LLM how to do something about fish maintenance that it does not know how to do, it might produce an answer like "Sure, first take your fish and " at which point all of the options for the next word are all over the place because there isn't the information available to guide the choice. The sentence started as if it knew the answer because there was no information to say that it didn't. By the time the absence of information has an impact, the LLM is already committed to the sentence where it is confidently giving you an answer.