The paper proposes a framework to study two-dimensional (2D) topologically ordered states subject to local correlated errors, leading to the emergence of *intrinsically mixed-state topological order* (imTO). The authors show that decoherence, previously interpreted as anyon condensation in a doubled Hilbert space, can be rephrased as "gauging out" anyons in the original Hilbert space. This process generically results in imTO, where the decohered mixed-state exhibits strong symmetry under certain anomalous 1-form symmetries. The framework connects the decohered density matrix to *topological subsystem codes* (TSSCs), which can appear as anomalous surface states of 3D topological orders. Through examples, the authors demonstrate that the decohered state can display classical memory, encode logical qubits (quantum memory), and host chiral or non-modular topological order. They argue that these decohered states represent genuine mixed-state quantum phases of matter and provide a partial classification of imTO in terms of braided fusion categories. The paper also discusses the stability of imTOs to finite-depth local quantum channels and their potential applications in quantum information processing.The paper proposes a framework to study two-dimensional (2D) topologically ordered states subject to local correlated errors, leading to the emergence of *intrinsically mixed-state topological order* (imTO). The authors show that decoherence, previously interpreted as anyon condensation in a doubled Hilbert space, can be rephrased as "gauging out" anyons in the original Hilbert space. This process generically results in imTO, where the decohered mixed-state exhibits strong symmetry under certain anomalous 1-form symmetries. The framework connects the decohered density matrix to *topological subsystem codes* (TSSCs), which can appear as anomalous surface states of 3D topological orders. Through examples, the authors demonstrate that the decohered state can display classical memory, encode logical qubits (quantum memory), and host chiral or non-modular topological order. They argue that these decohered states represent genuine mixed-state quantum phases of matter and provide a partial classification of imTO in terms of braided fusion categories. The paper also discusses the stability of imTOs to finite-depth local quantum channels and their potential applications in quantum information processing.