I know someone who generated thousands of links to facebook profiles, including non-linked ones. They crawled for images with facebook meta data, pulled the facebook IDs, and used those to generate the profile links.
I'm not able to verify this right now, but facebook stores user identification information using EXIF in JPEGs? If so, I wonder whether image hosts delete this info before hosting your file.
Actually, the user ID is in the photo URL. Well, at least it was some time ago.