Non-Hermiticity can do more than create isolated bound states in the continuum: under suitable conditions it can generate entire families of bound states and even yield anomalous extended states within an otherwise localized continuum. Here, we show that a second-order non-Hermitian skin effect (NHSE) can produce corner-localized modes whose eigenvalues remain embedded in the continuum of extended bulk bands. The key mechanism is an internal subspace structure revealed by an appropriate basis transformation, which decomposes the Hilbert space into two orthogonal subspaces: one supports second-order skin-induced corner modes, while the other hosts topologically trivial continuum bands with extended bulk states. This orthogonality suppresses hybridization between the corner modes and the continuum even when they overlap in energy. Moreover, the resulting corner-localized modes are robust against disorder, highlighting their topological protection. Our results establish a route to realizing a second-order NHSE embedded in the continuum and broaden the landscape of non-Hermitian topological phases.

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• Bound states in the continuum
• Skin effect
• Synthetic gauge fields
• Topological phases of matter
• Non-Hermitian systems