Safe Environment from Countries Under Repression and Emergency Act or the SECURE Act This bill permits a qualifying alien who is not inadmissible or deportable under certain criminal or security grounds or who did not participate in persecution to apply for adjustment to lawful permanent resident status if such alien: (1) is in temporary protected status (TPS), (2) held TPS status, (3) qualified for TSP status at the time of the Department of Homeland Security's (DHS) last TPS designation, or (4) is a national of a foreign country that was at any time a TPS-designated country. TPS designation permits eligible nationals of designated counties affected by armed conflict or natural disasters to temporarily reside and work in the United States. An alien who has applied for status adjustment may work while the application is pending. The spouse, domestic partner, child, or unmarried son or daughter of an alien who has adjusted to lawful permanent resident status may also adjust to such status subject to certain conditions. An unmarried son or daughter must additionally establish physical presence in the United States for at least one year. An alien subject to a final order of removal may not be removed if the alien has a pending status adjustment application or is prima facie eligible to file an application and indicates an intention to do so. An alien who raises the defense of status adjustment eligibility may not be removed unless DHS has already denied the alien's application.