  The inelastic collapse of stochastic trajectories of a randomly accelerated
particle moving in half-space $z > 0$ has been discovered by McKean and then
independently re-discovered by Cornell et. al. The essence of this phenomenon
is that particle arrives to a wall at $z = 0$ with zero velocity after an
infinite number of inelastic collisions if the restitution coefficient $\beta$
of particle velocity is smaller than the critical value
$\beta_c=\exp(-\pi/\sqrt{3})$. We demonstrate that inelastic collapse takes
place also in a wide class of models with spatially inhomogeneous random force
and, what is more, that the critical value $\beta_c$ is universal. That class
includes an important case of inertial particles in wall-bounded random flows.
To establish how the inelastic collapse influence the particle distribution, we
construct an exact equilibrium probability density function $\rho(z,v)$ for
particle position and velocity. The equilibrium distribution exists only at
$\beta<\beta_c$ and indicates that inelastic collapse does not necessarily mean
the near-wall localization.
