  Using the framework of supersymmetric non-linear $\sigma$-model we develop a
general non-perturbative characterisation of universal features of the density
$\rho(\Gamma)$ of the imaginary parts (``width'') for $S$-matrix poles
(``resonances'') describing waves incident and reflected from a disordered
medium via $M$-channel waveguide/lead. Explicit expressions for $\rho(\Gamma)$
are derived for several instances of systems with broken time-reversal
invariance, in particular for quasi-1D and 3D media. In the case of perfectly
coupled lead with a few channels ($M\sim 1$) the most salient features are
tails $\rho(\Gamma)\sim \Gamma^{-1}$ for narrow resonances reflecting
exponential localization and $\rho(\Gamma)\sim \Gamma^{-2}$ for broad
resonances reflecting states located in the vicinity of the attached wire. For
multimode quasi 1D wires with $M\gg 1$, an intermediate asymptotics
$\rho(\Gamma)\sim \Gamma^{-3/2}$ is shown to emerge reflecting diffusive nature
of decay into wide enough contacts.
