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But what I don't understand is that if you look at the cache, it shows the old page and a cache date that is after the date the file was removed.
The cache date should show a date prior to the file removal.
Is this common? Should I care?
I'd say most times cache date matches, but for pages linked from footer and those that do not change much Google does show a recent cache date while the actual crawl date is much older.
So things can be messed up with dates, and the date shown is the crawl date and not the date of the page.
Even so, why does my page show up which is not there? It was removed weeks before the crawl date. It seems like it visited the page, didn't find it and then placed in cache the last known copy.