Multi-label Out-Of-Distribution (OOD) detection aims to discriminate the OOD samples from the multi-label In-Distribution (ID) ones. Compared with its multiclass counterpart, it is crucial to model the joint information among classes. To this end, JointEnergy, which is a representative multi-label OOD inference criterion, summarizes the logits of all the classes. However, we find that JointEnergy can produce an imbalance problem in OOD detection, especially when the model lacks enough discrimination ability. Specifically, we find that the samples only related to minority classes tend to be classified as OOD samples due to the ambiguous energy decision boundary. Besides, imbalanced multi-label learning methods, originally designed for ID ones, would not be suitable for OOD detection scenarios, even producing a serious negative transfer effect. In this paper, we resort to auxiliary outlier exposure (OE) and propose an unknown-aware multi-label learning framework to reshape the uncertainty energy space layout. In this framework, the energy score is separately optimized for tail ID samples and unknown samples, and the energy distribution gap between them is expanded, such that the tail ID samples can have a significantly larger energy score than the OOD ones. What's more, a simple yet effective measure is designed to select more informative OE datasets. Finally, comprehensive experimental results on multiple multi-label and OOD datasets reveal the effectiveness of the proposed method.