This paper investigates the entanglement structure of topological orders subject to decoherence on the bipartition boundary, focusing on toric codes in 2, 3, and 4 space dimensions. The authors explore whether boundary decoherence can induce a disentangling transition, characterized by the destruction of long-range entanglement across the bipartition, measured by topological entanglement negativity. A key insight is the connection between the negativity spectrum of the decohered mixed states and emergent symmetry-protected topological (SPT) orders under certain symmetry-preserving perturbations localized on the bipartition boundary. This allows for the analytical derivation of entanglement negativity without using the replica trick. The study reveals that for the 2d toric code, the entanglement negativity relates to the free energy difference associated with prohibiting domain walls in a 1d Ising model, indicating the persistence of long-range entanglement up to maximal decoherence. In contrast, for the 3d toric code, the entanglement negativity relates to the partition function of a 2d classical $\mathbb{Z}_2$ gauge theory, which does not exhibit a finite-temperature transition, suggesting the persistence of long-range entanglement. However, for the 4d toric code, the entanglement negativity relates to the partition function of a 3d classical $\mathbb{Z}_2$ gauge theory, which exhibits a confinement-deconfinement transition, indicating a disentangling transition at a critical noise rate. The authors also discuss the implications of these findings for the understanding of mixed-state phases of matter and the potential connection to separability transitions and channel definitions. They suggest that further exploration of intrinsically mixed-state topological orders and other non-trivial states of matter subject to boundary decoherence could be fruitful.This paper investigates the entanglement structure of topological orders subject to decoherence on the bipartition boundary, focusing on toric codes in 2, 3, and 4 space dimensions. The authors explore whether boundary decoherence can induce a disentangling transition, characterized by the destruction of long-range entanglement across the bipartition, measured by topological entanglement negativity. A key insight is the connection between the negativity spectrum of the decohered mixed states and emergent symmetry-protected topological (SPT) orders under certain symmetry-preserving perturbations localized on the bipartition boundary. This allows for the analytical derivation of entanglement negativity without using the replica trick. The study reveals that for the 2d toric code, the entanglement negativity relates to the free energy difference associated with prohibiting domain walls in a 1d Ising model, indicating the persistence of long-range entanglement up to maximal decoherence. In contrast, for the 3d toric code, the entanglement negativity relates to the partition function of a 2d classical $\mathbb{Z}_2$ gauge theory, which does not exhibit a finite-temperature transition, suggesting the persistence of long-range entanglement. However, for the 4d toric code, the entanglement negativity relates to the partition function of a 3d classical $\mathbb{Z}_2$ gauge theory, which exhibits a confinement-deconfinement transition, indicating a disentangling transition at a critical noise rate. The authors also discuss the implications of these findings for the understanding of mixed-state phases of matter and the potential connection to separability transitions and channel definitions. They suggest that further exploration of intrinsically mixed-state topological orders and other non-trivial states of matter subject to boundary decoherence could be fruitful.