Unsupervised object discovery (UOD) aims to detect and segment objects in 2D images without handcrafted annotations. Recent progress in self-supervised representation learning has led to some success in UOD algorithms. However, the absence of ground truth provides existing UOD methods with two challenges: 1) determining if a discovered region is foreground or background, and 2) knowing how many objects remain undiscovered. To address these two problems, previous solutions rely on foreground priors to distinguish if the discovered region is foreground, and conduct one or fixed iterations of discovery. However, the existing foreground priors are heuristic and not always robust, and a fixed number of discoveries leads to under or over-segmentation, since the number of objects in images varies. This paper introduces UnionCut, a robust foreground prior based on ensemble methods that detects the union of foreground areas of an image, allowing UOD algorithms to identify foreground objects and stop discovery once the majority of the foreground union in the image is segmented. On top of that, we propose UnionSeg, a vision transformer distilled from UnionCut that outputs the foreground union faster and more accurately. Our experiments show that by combining with UnionCut or UnionSeg, previous state-of-the-art UOD methods witness an increase in the performance of single object discovery, saliency detection and self-supervised instance segmentation on various benchmarks. The code is available at https://anonymous.4open.science/r/UnionCut-6CFC/README.md.