Complex sentence: Many of the undocumented workers say they seek an asylum status under the Convention Relating to the Status of Refugees of the United Nations, but only a fraction of all the undocumented workers is actually eligible for this status (see Sudanese refugees in Israel).
Split into simpler sentences: Many of the undocumented workers seek an asylum status under the Convention Relating to the Status of Refugees of the United Nations. Only a fraction of all the undocumented workers is actually eligible for this status (see Sudanese refugees in Israel).