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Recently, weakly supervised person search is proposed to discard human-annotated identities and train the model with only bounding box annotations. A natural way to solve this problem is to separate it into detection and unsupervised re-identification (Re-ID) steps. However, in this way, two important clues in unconstrained scene images are ignored. On the one hand, existing unsupervised Re-ID models only leverage cropped images from scene images but ignore its rich context information. On the other hand, there are numerous unpaired persons in real-world scene images. Directly dealing with them as independent identities leads to the long-tail effect, while completely discarding them can result in serious information loss. In light of these challenges, we introduce a Context-Guided and Unpaired-Assisted (CGUA) weakly supervised person search framework. Specifically, we propose a novel Context-Guided Cluster (CGC) algorithm to leverage context information in the clustering process and an Unpaired-Assisted Memory (UAM) unit to distinguish unpaired and paired persons by pushing them away. Extensive experiments demonstrate that the proposed approach can surpass the state-of-the-art weakly supervised methods by a large margin (more than 5% mAP on CUHK-SYSU). Moreover, our method achieves comparable or better performance to the state-of-the-art supervised methods by leveraging more diverse unlabeled data. Codes and models will be released soon.