Just in case I ever forget (or if you get stuck on this), if you have a site you’re trying to either link to or shortlink to so you can post the link in a FB post and have the image automatically load, but for whatever reason it keeps saying “404 not found” in the FB post, do this:
First, go to the target URL and delete the cache for that page. Either reset the OutputCache duration, delete the cache from disk, etc.
Next, visit the Facebook Sharing Debugger and use it to navigate to the target link. Note any errors and correct them. If needed click the Scrape Again button to force Facebook to clear its own cache and re-read the target site.
These steps resolved the issue for me, now my link image associated with the target link appears in FB posts normally.