A Google Webmaster Help thread shares a sad story of one person who built up a site on a members.aol.com hosted service. Recently shut down their AOL Hometown, which is the host space for these sites and this person's site is archived locally, but the domain is gone forever.
What can he/she do to get Google and the other search engines to recognize that the old domain is now pointing to the new domain? In this case, not much. Since this person doesn't have the ability or control to set up a 301 redirect from the old domain to the new domain, there is currently no automated way for a search engine to know the domain name has moved.
JohnMu of Google shared the bad news but explained that he/she can go through the process of reaching out to those who use to link to the site and tell them it moved somewhere else. John said:
Alas, once the old hosting is no longer available, there's not much that can be done. Since you cannot redirect from the old URLs to the new ones, the best thing that you can do is to contact the people who have linked to your old site and ask them to change the link to your new one. This might also have a slightly additional effect in that people may promote your content for you after being nodded in your direction again :-).
This is just one more reason not to host on a free hosting service. In addition, it goes well with our early post today on domain names, in where if Google had a way to tell them in Webmaster Tools if a site was moved, maybe via a meta tag verification process, it could have saved these people.
Forum discussion at Google Webmaster Help.