Semantic segmentation methods typically perform per-pixel classification by assuming a fixed set of semantic categories. While they perform well on the known set, the network fails to learn the concept of objectness, which is necessary for identifying unknown objects. In this paper, we explore the potential of query-based mask classification for unknown object segmentation. We discover that object queries specialize in predicting a certain class and behave like one vs. all classifiers, allowing us to detect unknowns by finding regions that are ignored by all the queries. Based on a detailed analysis of the model's behavior, we propose a novel anomaly scoring function. We demonstrate that mask classification helps to preserve the objectness and the proposed scoring function eliminates irrelevant sources of uncertainty. Our method achieves consistent improvements in multiple benchmarks, even under high domain shift, without retraining or using outlier data. With modest supervision for outliers, we show that further improvements can be achieved without affecting the closed-set performance.