If an individual is eligible under subsection (b) of this section, the individual shall be issued and may cast a provisional ballot: at a polling place on election day; at an early voting center during early voting; or at the local board office in the county where the individual resides after the close of registration and before the closing of the polls on election day. An individual is eligible to cast a provisional ballot if: the individual declares in a written affirmation submitted with the provisional ballot that the individual is a registered voter in the State and is eligible to vote in that election; and the individual’s name does not appear on the election register; an election official asserts that the individual is not eligible to vote; or the individual does not have the necessary identification. In addition to the individuals who cast provisional ballots under subsections (a) and (b) of this section, any individual who appears to vote during a period covered by a court order or other order extending the time for closing the polls shall cast a provisional ballot. A provisional ballot cast under this subsection shall be separated and held apart from other provisional ballots cast by those not affected by the order.