Reference calculations for subthreshold $\Xi$ production

We present a minimal statistical model designed for the description of rare-hadron multiplicities in nucleus-nucleus collisions at energies below the threshold of the particle production in binary elementary collisions. Differences to more conventional canonical statistical model are explained. The minimal statistical model is applied to the description of multiplicity ratios involving $\Xi$ hyperons, which are measured by the HADES collaboration at GSI-SIS. It is argued that the HADES data cannot be reproduced by the model based on the statistical equilibrium and the strangeness conservation. The data remain underpredicted even when in-medium potentials acting on hadrons are taken into account. This hints to non-equilibrium production of the $\Xi$ hyperons and their continuous freeze-out.