  The consistency between eigenvalues calculated under open and periodic
boundary conditions, named as {\it bulk-bulk correspondence} ($\mathcal{BBC}$),
can be destroyed in systems with non-Hermitian skin effect (NHSE). In spite of
the great success of the generalized Brillouin zone (GBZ) theory in clean
non-Hermitian systems, the applicability of GBZ theory is questionable when the
translational symmetry is broken. Thus, it is of great value to rebuild the
$\mathcal{BBC}$ for disorder samples, which extends the application of GBZ
theory in non-Hermitian systems. Here, we propose a scheme reconstructing
$\mathcal{BBC}$, which can be regarded as the solution of an optimization
problem. By solving this optimization problem analytically, we reconstruct the
$\mathcal{BBC}$ and obtain the modified GBZ theory in several prototypical
disordered non-Hermitian models. The modified GBZ theory gives a precise
description of NHSE, which predicts the intriguing disorder-enhanced and
disorder-irrelevant NHSEs.
