The deployment of machine learning solutions in real-world scenarios often involves addressing the challenge of out-of-distribution (OOD) detection. While significant efforts have been devoted to OOD detection in classical supervised settings, the context of weakly supervised learning, particularly the Multiple Instance Learning (MIL) framework, remains under-explored. In this study, we tackle this challenge by adapting post-hoc OOD detection methods to the MIL setting while introducing a novel benchmark specifically designed to assess OOD detection performance in weakly supervised scenarios. Across extensive experiments based on diverse public datasets, KNN emerges as the best-performing method overall. However, it exhibits significant shortcomings on some datasets, emphasizing the complexity of this under-explored and challenging topic. Our findings shed light on the complex nature of OOD detection under the MIL framework, emphasizing the importance of developing novel, robust, and reliable methods that can generalize effectively in a weakly supervised context. The code for the paper is available here: https://github.com/loiclb/OOD MIL.