Deep unfolding networks (DUNs) have recently advanced concealed object segmentation (COS) by modeling segmentation as iterative foreground-background separation. However, existing DUN-based methods (RUN) inherently couple background estimation with image restoration, leading to conflicting objectives and requiring pre-defined degradation types, which are unrealistic in real-world scenarios. To address this, we propose the nested unfolding network (NUN), a unified framework for real-world COS. NUN adopts a DUN-in-DUN design, embedding a degradation-resistant unfolding network (DeRUN) within each stage of a segmentation-oriented unfolding network (SODUN). This design decouples restoration from segmentation while allowing mutual refinement. Guided by a vision-language model (VLM), DeRUN dynamically infers degradation semantics and restores high-quality images without explicit priors, whereas SODUN performs reversible estimation to refine foreground and background. Leveraging the multi-stage nature of unfolding, NUN employs image-quality assessment to select the best DeRUN outputs for subsequent stages, naturally introducing a self-consistency loss that enhances robustness. Extensive experiments show that NUN achieves a leading place on both clean and degraded benchmarks. Code will be released.