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This is a great answer, and holy crap on the Washington Post for getting all the major details wrong. So this is ONLY relevant to immigrants that enter the country illegally. If you enter the country legally, as in the case of any VISA (student, tourist, au-pair, etc etc) then even if you overstay your VISA you do not (and should not) leave the country before or during the application process. This is only relevant to those who entered without a visa.
They received it three days after i sent it.. it doesn't take USPS more than three days to deliver a piece of mail to my local field office. You're not focusing on the question though: regardless of when I sent it, when I see both of these statements on the website, how should i read it?