Concealed object segmentation (COS) is a challenging problem that focuses on identifying objects that are visually blended into their background. Existing methods often employ reversible strategies to concentrate on uncertain regions but only focus on the mask level, overlooking the valuable of the RGB domain. To address this, we propose a Reversible Unfolding Network (RUN) in this paper. RUN formulates the COS task as a foreground-background separation process and incorporates an extra residual sparsity constraint to minimize segmentation uncertainties. The optimization solution of the proposed model is unfolded into a multistage network, allowing the original fixed parameters to become learnable. Each stage of RUN consists of two reversible modules: the Segmentation-Oriented Foreground Separation (SOFS) module and the Reconstruction-Oriented Background Extraction (ROBE) module. SOFS applies the reversible strategy at the mask level and introduces Reversible State Space to capture non-local information. ROBE extends this to the RGB domain, employing a reconstruction network to address conflicting foreground and background regions identified as distortion-prone areas, which arise from their separate estimation by independent modules. As the stages progress, RUN gradually facilitates reversible modeling of foreground and background in both the mask and RGB domains, reducing false-positive and false-negative regions. Extensive experiments demonstrate the superior performance of RUN and underscore the promise of unfolding-based frameworks for COS and other high-level vision tasks. The source code will be made publicly available.