Do you mean the Ethiopian Jews? They were flown out of that country by the Israeli government (it was a difficult operation because surrounding countries are very hostile to Israel) and brought to live in Israel. They do face some racism, but their lives are much better than in Ethiopia.
I think the lineage is supposed to come from an alleged son of King Solomon with the Queen of Sheba.
The TV show said another group, not in Ethiopia, has always claimed to be part of the lost tribe but that claim has never been proven. Some scientists went in and took DNA samples from them and compared them to Jewish rabbis in Israel. They had the same markers so it was proven in their case.