The Board has announced that because of the shutdown and the BIA’s zip code change, which happened at the same time, it will consider all filings received by the Board before November 1, 2013┬áto be timely filed.
So, if you had something due during the shutdown that either wasn’t received or was received late by the Board, you are in the clear as long as the Board receives it before November 1, 2013.

Here is their announcement:

The Board of Immigration Appeals (BIA) processed only filings related to detained cases during the lapse in government funding. The BIA did accept all filings during that period. Also, as announced in September, EOIR transitioned to zip code 20530 on October 1, 2013.

Due to the convergence of those two events, the BIA will consider timely filed any filing that meets both of these criteria: the filing was due during the month of October 2013; and the BIA receives the filing on or before November 1, 2013.

No request for, or documentation supporting, an extension is required for filings that arrive at the BIA by November 1, 2013. Filings that arrive after November 1, 2013, are subject to normal filing deadlines. If timeliness is an issue for any filings that the BIA receives after November 1, 2013, parties should consult the BIA Practice Manual for guidance.