On Stack Exchange, users gain valuable Internet points (reputation) when their questions or answers are upvoted and lose (fewer) points when they're downvoted. This creates an incentive to try to answer any question where you can expect a net-positive change in score.
Some questions are really, clearly not good fits for the site -- they're off-topic, or they don't provide nearly enough detail, or they're otherwise pretty obviously on the road to being put on hold. Once a question is put on hold no new answers can be added until the question is edited (if it can be) and reopened. Questions are put on hold (and reopened) by user vote or by moderators.
On one site that I'm involved with, we have a widespread pattern of users rushing to answer questions that are, soon thereafter, put on hold. Sometimes these answers give good advice -- but it's advice about things that shouldn't have been asked on that site in the first place. Because it's good advice, it gets voted up even after the question is put on hold.
Sometimes several hours elapse between when such a question is asked and when it's put on hold, but I've seen this happen in under 15 minutes so I don't think "close faster" is an option. Our community is reasonably diligent here already, but also pretty popular, so stuff will get through.
Moderators (or, sometimes, users or automated processes) can delete these questions eventually, but I'm not looking for ways to clean it up -- I'm looking for a way to get users to not answer doomed questions in the first place. I realize it's their time to waste, but sometimes this situation creates drama when a question is deleted and people who answered it lose reputation points. Secondarily, it's harder to edit a question that's been put on hold to fix it if there are already answers; we try not to invalidate existing answers, though in some cases we do that anyway and edit the affected answers.
How can we get users to set aside their own possible reputation gain and instead vote to put on hold questions that do not fit in their current form? I am looking for a behavioral solution, not a technical one.