There are 2 questions on down-votng and closed questions.
Is it POSSIBLE to down vote a question after the question is closed?
Also, is it required that the question CAN be down voted after the question is closed?
It is possible to vote on a closed question and its answers. In particular, it is possible to downvote the question, but it's also possible to upvote it.
A different question would be: is it desirable to downvote a question after it's closed? It's a matter of opinion, and mine is that, if the question score is already negative, there is no reason to pile on downvotes.