/ AbstractThe HADES data from p+Nb collisions at center of mass energy of $\sqrt{s_{NN}}$= 3.2 GeV are analyzed by employing a statistical model. Accounting for the identified hadrons $π^0$, $η$, $Λ$, $K^{0}_{s}$, $ω$ allows a surprisingly good description of their abundances with parameters $T_{chem}=(99\pm11)$ MeV and $μ_{b}=(619\pm34)$ MeV, which fits well in the chemical freeze-out systematics found in heavy-ion collisions. In supplement we reanalyze our previous HADES data from Ar+KCl collisions at $\sqrt{s_{NN}}$= 2.6 GeV with an updated version of the statistical model. We address equilibration in heavy-ion collisions by testing two aspects: the description of yields and the regularity of freeze-out parameters from a statistical model fit. Special emphasis is put on feed-down contributions from higher-lying resonance states which have been proposed to explain the experimentally observed $Ξ^-$ excess present in both data samples.