Spectral stability captures behavior of a solution perturbed by an infinitesimal perturbation. It often determines nonlinear stability but it is limited to the exact form of the dynamics of the system. However, governing equations are often only an approximation of a larger system that models real world situation. We show how are the spectral stability of a solution in the reduced and full (extended) system related, particularly for ODEs in the case of frequently used quasi-steady-state reduction but also in a general case of reduced/extended system. A connection is also drawn with the geometric Krein signature that is shown to naturally characterize spectral properties under such extensions.