I like this proposal, seems useful to promote the usage of down-voting, but some considerations have to be made since when down-voting we are stating that:
This question does not show any research effort; it is unclear or not useful (click again to undo)
So, the down-vote alone will start being used even if the question demonstrates efforts from the user to achieve is goal.
It is necessary to consider that questions may get closed by being exact duplicates or off topic, that doesn't necessarily mean that the user haven't sweated to try to solve the issue:
This question covers exactly the same content as earlier questions on this topic; its answers may be merged with another identical question.
Questions on Stack Overflow are expected to relate to programming or software development within the scope defined in the FAQ. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about closed questions here.
I like this solution if practicably applied to situations where the down-voter gets rewards if the question gets closed under this grounds:
As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or specific expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, see the FAQ for guidance.
not a real question
It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.
Questions closed by `too localized` option
This is grounds for a deeper discussion, but my first choice would be to exclude the awards on this topic.
Deleted questions should reward the down-voters since if the question got deleted, the community agrees that it was a really a bad question!
See the FAQ, where it reads:
Questions that are extremely off topic, or of very low quality, may be removed at the discretion of the community and moderators.