; and (2) by inserting after subparagraph (A) the following new subparagraphs: (B) To the extent that the program carried out by a State under subparagraph (A) to systematically remove the names of ineligible voters from the official lists of eligible voters uses information obtained in an interstate cross-check, the State may not remove the name of the voter from such a list unless— (i) the State obtained the voter’s full name (including the voter’s middle name, if any) and date of birth, and the last 4 digits of the voter’s social security number, in the interstate cross-check; or (ii) the State obtained documentation from the ERIC system that the voter is no longer a resident of the State. (C) In this paragraph— (i) the term interstate cross-check means the transmission of information from an election official in one State to an election official of another State