I can't think of any examples yet where a DC has done this, but I've had dream content in non-lucid dreams that I later discovered was based on stuff I consciously thought I had forgotten, or didn't even know I knew.
For me it hasn't happened a lot while lucid but yeah, seems like for most its more likely to happen in non lucid dreams.

I definitely have been wanting to ask DCs about myself and maybe about past events. It sometimes takes several attempts. In some recent ones, the DCs simply wouldn't talk (which is a bit unusual), and a lot of times I get DCs that respond more like software chatterbots than sentient people. On one occasion, I actually got a conversation that was more meaningful, though when I woke up I realized the DC really only told me what I already believed was the case. I'll keep trying, though.
XD I wonder what the dream world would be like if every dream character gave meaningful conversations. Probably would be really mind boggling. But if there are dream characters that tell us what we already believe to be the case and those that can change our opinions, than perhaps it is possible for them to use what is known to bring out snippets of information.

But the question is how. By asking a simple question or perhaps by a simple thought? I've found that questions, even the simplest, can often lead to unhelpful answers. But when asking these questions i viewed who i was asking nothing more than a dc i just met that could probably give me a correct answer. Which was a mistake. Because in dreams what you expect, even if a possibility, can lead to the conclusion you didn't want. To know the answer will be given is better.

Also, the character can reply the answer because of what you expect but from that you probably could get something thrown out that you didn't expect. However, its a different story if you ask a dc something beyond dreaming related. ^^