  Motivated by the phenomenon of Coherent Perfect Absorption, we study the
shape of the deepest minima in the frequency-dependent single-channel
reflection of waves from a cavity with spatially uniform losses. We show that
it is largely determined by non-orthogonality factors $O_{nn}$ of the
eigenmodes associated with the non-selfadjoint effective Hamiltonian. For
cavities supporting chaotic ray dynamics we then use random matrix theory to
derive, fully non-perturbatively, the explicit probability density ${\cal
P}(O_{nn})$ of the non-orthogonality factors for systems with both broken and
preserved time reversal symmetry. The results imply that $O_{nn}$ are
heavy-tail distributed, with the universal tail ${\cal P}(O_{nn}\gg 1)\sim
O_{nn}^{-3}$.
