  We study energy minimized configurations of amorphous solids with a simple
shear degree of freedom. We show that the low-frequency regime of the
vibrational density of states of structural glass formers is crucially
sensitive to the stress-ensemble from which the configurations are sampled. In
both two and three dimensions, a shear-stabilized ensemble displays a
$D(\omega_{\min}) \sim \omega^{5}_{\min}$ regime, as opposed to the
$\omega^{4}_{\min}$ regime observed under unstrained conditions. We also study
an ensemble of two dimensional, strained amorphous solids near a plastic event.
We show that the minimum eigenvalue distribution at a strain $\gamma$ near the
plastic event occurring at $\gamma_{P}$, displays a collapse when scaled by
$\sqrt{\gamma_P - \gamma}$, and with the number of particles as $N^{-0.22}$.
Notably, at low-frequencies, this scaled distribution displays a robust
$D(\omega_{\min}) \sim \omega^{6}_{\min}$ power-law regime, which survives in
the large $N$ limit. Finally, we probe the universal properties of this
ensemble through a characterization of the second and third eigenvalues of the
Hessian matrix near a plastic event.
