Can a part of the territory of the European Union be turned into a “non-territory” where the fundamental rights of the migrants and asylum seekers to appeal and to remain in their destination country while their applications are examined, and the right for an individual assessment in line with international standards, are as it were contracted, owing to the very attributes of this “non-territory”? This article argues that the Pact on Migration and Asylum, in particular with the pre-entry screening and the new border procedures, subtly develops and consolidates policies and rules aimed at “deterritorializing” the territory of the EU while reinforcing its practices of externalization. Moreover, this unprecedented deterritorialization-externalization combination, in order to produce tangible policy results, presupposes the cooperation of third countries on expulsion and readmission, as well as more solidarity among the Member States. Having critically examined these two dimensions, the authors conclude that the new measures contained in the Pact might be conducive to the enhanced precarization of the legal positions of migrants and asylum seekers and to potential tensions with strategic third countries.