The First Circuit has determined that a person who reenters the United States illegally after being deported, and whose order of removal is reinstated by the Department of Homeland Security, is not eligible for asylum. The person, if found to have a reasonable fear of persecution or torture by an Asylum Officer, is permitted to apply for withholding of removal and protection under the Convention Against Torture before an Immigration Judge.
The full text of Garcia Garcia v. Sessions can be found here:
http://media.ca1.uscourts.gov/pdf.opinions/15-2571P-01A.pdf