An answer I deleted immediately after posting has been down-voted. Is this possible, or did the down-vote occur in the split-second before I deleted it?
If a user that can see deleted posts tries to downvote one, they will get the message:
This post has been deleted; deleted posts can't be voted on
However, due to a
known bug horrible design choice in the system, the system will sometimes automatically give downvotes, which is what probably happened here.
If you post a very short answer with no explanation, there's a good chance a system bot will flag it as "potentially low quality" for users to review.
if that flag is marked helpful, the system will cast a downvote on the post.
When your answer was deleted, the system went "Ha! That answer was deleted. Clearly I was right about the flag." And marked it as helpful.
Soooo... I guess don't delete posts immediately after posting them? It's also a good idea to add an explanation along with your answer to avoid having it marked as low quality.
Ideally, you shouldn't need to worry about that, but that feature was designed with Stack Overflow in mind (where it makes more sense), and the chances of us having it fixed to be non-stupid for this site are slim to none.