Each year in January, volunteers in and around Chicago canvass streets and parks to count people experiencing homelessness outside. This event, called the Point-in-Time (PIT) Count, is a biannual requirement for recipients of federal homeless assistance funding. Reporting on PIT Count data communicates the scope and demographics of homelessness in the United States on a given night to politicians and the public. In this paper, drawing from my ethnography of two PIT Counts in Chicago and Suburban Cook County, I contemplate how space is imagined in the PIT Count’s methods in both narrative and on the ground. I begin by arguing that fixing people in space and time during the PIT Count constructs a narrative that makes the state accountable in ending homelessness. I then argue that this rendering of space in narrative produces an impossible task for practitioners who must count homelessness on the ground. Rather than get bogged down in trying to delimit spatial boundaries around homelessness, I argue that PIT Count enumerators adapt by “feeling” out vulnerability in the moment and using their discretion in alignment with political objectives. I conclude by considering what could be gained in reimagining space at the site of contact in terms of continuum rather than a container. In paying ethical attention to spatial relations of contact during the PIT Count, I argue that enumerators understand vulnerability and exposure as interrelational. Reimagining space during contact brings attention to the social bonds that become threatened by insufficient materials for living.