On this question Are Soldiers Overdiagnosed with PTSD in the US Military? there is an answer which I think is of high quality and is valuable but doesn't actually answer the question. It simply provides evidence that indicates the claim could be true and then references a source that states there isn't really enough evidence to say for or against but then even directly states the claim is true.
Now, upon reflection I feel this warrants a down-vote simply for stating an answer without good evidence but to move anyway from this particular case; How should answers that don't fully answer the question but are constructive be handled. Bearing in mind that when you hover over the down-vote button it states "The answer is not useful". So if the answer (or question) is useful, it shouldn't be down-voted?