Foreign nationals may remain in the United States while an extension of an H1-B is pending with Citizenship and Immigration Service. If the extension is approved, and the extension application was filed before the I-94 expired, foreign nationals will not accrue any unlawful presence in the United States.
Unfortunately it is a policy of Immigration that if the H1-B extension is denied (even years later) the period of time from the I-94 expiration marks the time that the foreign national began to accrue unlawful presence. Because there are serious consequences to being in the United States with unlawful presence, including not being able to change to any other status, I strongly suggest you consult with an immigration attorney. During that consultation, the professional can offer you legal advice as opposed to the general information provided here.
This attorney is Board Certified, speaks Spanish and French, and represents clients throughout the United States. For other information, click through to the Blog.
Elizabeth R. Blandon