Homelessness is a social condition that jeopardises human dignity. Scientific literature to date has shown an increase in the number of homeless inhabiting streets and temporary shelters around the world. Such studies underlie the urge to address the homelessness phenomenon however, although they highlight the importance of overcoming this social issue, they lack up-to-date data and consensus about measurements to face this matter. Accordingly, the aim of this paper is to deepen the discussion of homelessness using a system thinking analysis. For this purpose, the city of Medellin in Colombia was chosen as a case study. We propose a new dynamic hypothesis based on the economic criminal careers developed in the literature. We use a causal-descriptive model that serves to illustrate the reasons for resistance to policies among homeless and the pathways that have led these people to reach such a condition. This analysis shows that there are programs to reduce homelessness in the long-term but are undermined by sort-term fixes. We suggest using this systemic analysis to build a simulation model that could be used as a tool for policy makers to assess new social policies focused on addressing homelessness.