A statistical-type model is developed to describe the ion production and electron emission in collisions of (molecular) ions with atoms. The model is based on the Boltzmann population of the bound electronic energy levels of the quasi molecule formed in the collision and the discretized continuum. The discretization of the continuum is implemented by a free electron gas in a box model assuming an effective square potential of the quasi molecule. The temperature of the electron gas is calculated by taking into account a thermodynamically adiabatic process due to the change of the effective volume of the quasi molecule as the system evolves. The system may undergo a transition with a small probability from the discretized continuum to the states of the complementary continuum. It is assumed that these states are decoupled from the thermodynamic time development. The decoupled states overwhelmingly determine the yield of the asymptotically observed fragment ions. The main motivation of this work is to describe the recently observed $H^-$ ion production in $OH^+ + Ar$ collisions. The obtained differential cross sections for $H^-$ formation, cation production and electron emission are close to the experimental ones. Calculations for the atomic systems $O^+ + Ar$ and $H^+ + Ar$ are also in reasonable agreement with the experiments indicating that the model can be applied to a wide class of collisions.