“The following were those who came up from Tel-melah, Tel-harsha, Cherub, Addon, and Immer, but they could not prove their ancestral houses or their descent, whether they belonged to Israel. The descendents of Delaiah, the descendents of Tobiah, and the descendents of Nekoda were six hundred forty-two. Also, of the priests were the descendents of Hobaiah, the descendents of Hakkoz, and the descendents of Barzillai. They had married one of the daughters of Barzillai the Gileadite and were called by their name. These sought their registration among those enrolled in the genealogies, but it was not found there. Thus they were excluded from the priesthood as unclean. The governor told them that they were not to partake of the most holy food, until a priest with Urim and Thummim should come.”
Once again, this is almost word for word from Ezra, chapter 2. This poses a dilemma. What if you could not prove that you were an Israelite? Could you say you wanted land in Israel without being an Israelite? Apparently there were some genealogical records that could be consulted. Like many things, they may not have been 100% accurate. There is a slight difference in the number of people in the category of whether they were Israelites, with 642 here as opposed to 652 in Ezra. The second group claimed to be priests. In the first group the only slight discrepancy is with Addon instead of Addan, while in the 2nd group there is Hobaiah instead of Habaiah. Barzillai had been a friend of King David. I believe that the only questions here were how these people were related to the groups that they claimed that they were from. The unnamed governor told them that they had to consult with a priest because they were unclean. The priests would go to the lots of Urim and Thummim. Urim and Thummim were in the breastplate of the ephod that the priests wore. They would consult with these stones on the breastplate to find out the will of Yahweh on what was to be done. Generally one was positive and the other negative. In fact, this was one of the ways that Yahweh communicated with his people. The other 2 ways were through dreams and prophets, which was also common among the Assyrians and Babylonians. This third way was like the tablets of destiny in Babylonia. Sometime in Jewish history it died out as a usage. However, this mysterious Urim and Thummim have found their way into novels and the writings of Joseph Smith, the first Mormon.