Extending Status Protection for Eligible Refugees with Established Residency Act of 2017 or the ESPERER Act of 2017 This bill permits a qualifying national of Haiti, Nicaragua, El Salvador, or Honduras who is in temporary protected status (TPS) to apply for adjustment to lawful permanent resident status before January 1, 2021. TPS designation permits eligible nationals of designated countries affected by armed conflict or natural disasters to temporarily reside and work in the United States. The spouse, 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 alien subject to a final order of removal may seek a stay of such order based on the filing of an application for status adjustment.