The presence of clusterlike narrow resonances in the vicinity of reaction or decay thresholds is a ubiquitous phenomenon with profound consequences. We argue that the continuum coupling, present in the open quantum system description of the atomic nucleus, can profoundly impact the nature of near-threshold states. In this Letter, we discuss the structure of the recently observed near-threshold resonance in B11, whose very existence explains the puzzling beta-delayed proton emission of the neutron-rich Be11.