URLs with ' at the end

Google is reporting errors with URLs that have an apostrophe at the end
of the URL and reporting it as a 404. Which is right because none of
the URLs use an apostrophe at the end, example http://www.mysite.com/'.
Notice the apostrophe at the end. Today I just noticed that the home
page has an error because it's using an apostrophe. My concern is that
Google considers this URL the same as the real URL.

Has this happened to anybody?
Will Google remove the real URL from its index?