This question already has an answer here:
Users with the trusted user privilege (20k rep on most sites, 4k on beta sites) get some handy extra powers. Among them are:
- Voting to delete answers with score of -1 or lower
- Voting to delete questions with a score of -3 or lower immediately after they are closed
Both of those abilities depend on the post score, so, if the post is just one downvote away from being eligible for deletion, as a 20k user I can just downvote it, refresh the page and vote to delete it. This is pretty useful, especially when cleaning up useless crap answers, since those often have no upvotes or downvotes (because most people rarely downvote), and thus sit at score 0.
The only annoying bit in the process is the extra page refresh needed to actually bring up the "delete" link. There's no real technical reason for it — the AJAX back-end can accept a delete vote just fine as soon as the post has been downvoted. It's only the link that's missing from the UI.
(And yes, it really is just the link that's missing; the scripts needed to make it work are already there. If you use developer tools to copy a delete link from another post, and just change the post ID, it will work just fine.)
If downvoting a post makes it eligible for delete votes, please make the "delete" link appear immediately, without requiring a page refresh.