Homelessness, a long-standing societal problem, appears to be on the rise, fueled in part by the Covid-19 pandemic. Looking at the homelessness system as a network of interconnected services which individuals traverse over time, we seek to shed light on their progression toward securing stable housing. We formalize the concept of stability upon exit and show that regardless of starting conditions, the ultimate goal is either reached quickly or not at all, indicating the importance of addressing the homeless’ needs early on to avoid them “giving up.” To better understand the causes that may contribute to positive outcomes for certain individuals versus others, we computationally analyze their pathways through the network of homeless services. We confirm the intuition that some individuals face more challenges than others based on their initial living conditions and initial placement to homelessness services. At the same time, we discover that simple signals can act as good indicators of individuals at risk of “falling through the cracks.” Being able to predict such outcomes is critical to design assistive technology that can retain individuals who would otherwise falter.