Sometimes, really interesting questions surface that end up getting quickly and heavily downvoted and close-voted, simply because they were so poorly written, showed no evidence of research, etc. Then someone comes along, gives the entire thing a makeover and, while the original downvotes never quite go away, the question gets an entirely new lease of life (and in that specific case1 even made it to hot network questions).
But other times, these questions end up getting closed and deleted through the moderation process, or deleted by the owner before anyone has had a chance to salvage it, either out of shame and/or because they didn't know how to fix it and saw no other way out. Which is understandable — the damage had been done. Recently I witnessed a case of precisely this, and it was unfortunate because the question had come from a user with a history of asking poor questions, so it was entirely understandable they didn't know what to do.
I could vote to undelete the question, but the fact that it was so poorly written at the time of deletion makes it unlikely anyone else would want to save it. Editing it while deleted isn't going to make the downvotes go away, and those downvotes will only generate unnecessary commotion for as long as they aren't yet offset by upvotes ("why was such a good question downvoted so horribly?" "Because it was originally a horrible question" "why couldn't someone have just fixed it for the OP?" "I wanted to but then it got closed and deleted" and so on). And besides, I've been leaning towards just respecting the owners' decisions in such cases.
What if I repost it as new, would that be fine? I can acknowledge the original post, but I have no idea if I should refer to them by name or if I should leave their name out, and on top of that, I don't know if the community sees this information as noise. I can post the question as though none of this had happened, but I don't know if anyone who had seen the original question would give me hell for taking credit for someone else's ideas (obviously this would be a different set of people from those who would consider it noise).
1 If you notice, my answer to that question arrived very late. That's because I never saw the question at the time it was asked, precisely because it was already so heavily downvoted to the point of escaping my front page never to come back. I had answered a duplicate question instead, and I opted to merge both questions seeing as they were nearly word-for-word identical, and the existing answer to the original question basically says "I don't have much to go on but this is what it looks like" — I was one of the only users in any position to answer the question authoritatively.