There are different phenomena that may have an impact on poverty levels, and migration is one of them. In part, this happens due to the selectivity of migration, which we discuss theoretically and empirically in this paper. We propose a theoretical model, based on the Roy and the human capital models, which gives particular attention to the poorest individuals. Based on the mathematical equations of this theoretical model, we present some simulations that address different aspects that may possibly promote the existence of territorial poverty traps. Moreover, with the use of multinomial logistic models, we observe a general tendency of negative selection for migrants in rural/rural flows and a positive one in rural/urban and longer steps of migration. That is, poor migrants in rural areas have a limited range of options whether and/or where to migrate and are partially trapped in their origin.