When the Jews returned from the captivity in Babylon, Nehemiah determined the true lineage of each Jewish family based on witnesses.
Without the genealogical records that were lost when the Temple was burned, they couldn't determine who truly belonged to the priesthood "till a priest could consult with the Urim and Thummim" Ezra 2:63.
They hope this will happen when Elijah returns with the breastplate of the High Priest.