  We study the properties of eigenvalues and corresponding eigenfunctions
generated by a defect in the gaps of the spectrum of a high-contrast random
operator. We consider a family of elliptic operators $\mathcal{A}^\varepsilon$
in divergence form whose coefficients are random, possess double porosity type
scaling, and are perturbed on a fixed-size compact domain (a defect). Working
in the gaps of the limiting spectrum of the unperturbed operator
$\hat{\mathcal{A}}^\varepsilon$, we show that the point spectrum of
$\mathcal{A}^\varepsilon$ converges in the sense of Hausdorff to the point
spectrum of the limiting two-scale operator $\mathcal{A}^\mathrm{hom}$ as
$\varepsilon \to 0$. Furthermore, we prove that the eigenfunctions of
$\mathcal{A}^\varepsilon$ decay exponentially at infinity uniformly for
sufficiently small $\varepsilon$. This, in turn, yields strong stochastic
two-scale convergence of such eigenfunctions to eigenfunctions of
$\mathcal{A}^\mathrm{hom}$.
