Remember that there are several types of Supplemental Results.
For a page that goes 404 or the domain expires, Google keeps a copy of the very last version of the page that they saw, as a Supplemental Result and show it in the index when the number of other pages returned is low. The cached copy will be quite old.
For a normal site, the current version of the page should be in the normal index, and the previous version of the page is held in the Supplemental index.
If you use search terms that match the current content, then you see that current content in the title and snippet, in the cache, and on the live page.
If you search for terms that were only on the old version of the page, then you see those old search terms in the title and snippet, even though they are not in the cache, nor found on the live page. That result will be marked as Supplemental.
There are also supplemental results where the result is for duplicate content of whatever Google considers to be the "main" site. These results seemingly hang around forever, with an old cache, a cache that often no longer reflects what is really on the page right now. Usually there is no "normal" result for that duplicate URL - just the old Supplemental, based on the old data. On the other hand, the "main" URL will usually have both a normal result and a Supplemental result (but not always).
Right now I see some interesting bugs in the Supplemental logic.
site:domain.com inurl:www brings 98000 www pages all with a recent cache.
site:domain.com -inurl:www brings 24000 www pages (even though the search says to exclude all www pages) all of them marked as Supplemental and all showing a cache date of almost a year ago.
That should not be happening.
Add to that the pages with meta robots noindex tags on them that have been indexed and cached, and are showing as Supplemental Results with a cache from 2005 June or July, and Google has a bit of a problem on their hands right now.
Oh, and searches with a hyphen in them are not fixed either. Search for an email address with a hyphen in it. See what results you get. Search again, replacing the hyphen with a space and see that thousands of supplemental pages appear from nowhere - all for pages that have (or had) the email address printed on them at some time.