I have a massively downvoted question with no answers and already has 2 votes to close. Does closing or deleting both refund my reputations lost?
No, closing a question has no effect on your reputation, regardless of whether it is closed by you, by others, or by a moderator. Only deletion refunds lost reputation, and it refunds it regardless of who deleted it or why.
Things to note:
- Posts deleted via a red flag (Spam or Rude or Abusive) incur a 100 rep penalty. You still get the rep from the downvotes back, but you also get a -100 hit to your rep, so in effect you will probably not get much rep.... The majority of deleted posts are not deleted via red flag, so unless you are posting ads for dietary supplements, hate speech, or word salad, you are probably safe from this.
- To be clear, red flaggable posts are considered much more harmful than regular posts that should be deleted - the threshold is much more than "this post should be removed". Off-topic questions, poorly-researched questions, wrong answers, poorly-researched answers, and comments posted as answers are regular low quality posts and, if deleted, are deleted through the regular processes that do not give a -100 rep penalty. Red flags are an exception to the rule - a way to get horrible posts off the site quickly.
- Question closure may push you closer to a Post Ban, but the details have not been made public so it is unclear if it truly does.
You do not regain reputation from voting to close the question, or having it closed, on their own.
However, once a question is closed, it becomes possible for users with high reputation to begin voting to delete it, which means that even if you can't delete it because there is an upvoted answer or multiple answers, those high-rep users can still vote to delete it, and if there are enough votes, it will be deleted, refunding the reputation.
Keep in mind, however, that the question will count negatively toward you in terms of post bans, as well as put a dent in your overall question record (questions that are downvoted, closed, and deleted count three times against you).