Refugee Protection Act of 2019 This bill provides protections for aliens such as asylum seekers and contains other provisions. The bill's provisions include eliminating the general requirement that an asylum seeker apply for asylum within one year of arriving in the United States; prohibiting requiring an asylum seeker to provide corroborating evidence of persecution if such evidence is not reasonably obtainable; waiving certain grounds of inadmissibility or deportability for qualifying refugees seeking permanent resident status; requiring the Department of Justice to appoint counsel to a child or particularly vulnerable individual in certain immigration proceedings; increasing the annual cap on principal nonimmigrant U visas (victims of crimes) from 10,000 to 20,000; prohibiting the removal of an alien with certain pending immigration applications, such as a U visa application; imposing limits on when an alien may be removed from the United States in a proceeding without the alien present; establishing a presumption that the least restrictive conditions necessary should be imposed in custody proceedings for asylum seekers, including release if appropriate; establishing that the maximum number of refugees admitted each fiscal year shall be no less than 95,000; directing the Department of State to help other governments increase their capacity to care for and accept refugees; directing the State Department to establish refugee processing centers in other countries in North and Central America; and authorizing the Department of Homeland Security to provide special immigrant status to qualified aliens who assisted U.S. efforts in Syria and admit up to 5,000 such aliens each fiscal year for five years.