[derekmhewitt]

This actually happened in WW2, after fully breaking the Enigma codes the Allies had to carefully choose which intelligence to act on and not act on, sometimes with poor results for their own side. But the alternative would have been that the Germans would have to conclude their communications were compromised and change something, rendering a lot of the effort to crack enigma in the first place moot. The Turing movie mentioned in another comment is excellent and touches on this topic.