Since 2015–2016, in the context of the so-called ‘refugee crisis’, new asylum policies altered the landscape of accommodation, housing, displacement, and (il)legalisation in Greece. This paper aims to explore the impact that the reception system established in 2016 has on everyday accommodation and urban experiences of refugees as regards their relationships with space and social connections. In doing so, it brings to the forefront the concept of ‘displaceability’ as an ongoing, non-linear, and relational sociospatial process, interrelated with housing precarity and illegalisation, through which the connections between people and places are ruptured. The paper, first, focuses on how processes and experiences of displaceability emerge for those entitled to asylum accommodation in Greece. Secondly, it examines how displaceability also concerns displaced people found at the margins of accommodation after their asylum claim has been processed, including both the cases of recognised beneficiaries of international protection and refugees with a negative decision. Thirdly, it discusses aspects of the experiences of those outside the reception system and accommodation sites, such as people arriving in Athens through informal and unregistered mobilities. The paper is based on research conducted in metropolitan Athens, Greece, as part of the TRAFIG Horizon 2020 research project.