A novel, unorthodox picture of the dynamics of heavy ion collisions is developed using the concept of Hagedorn states. A prescription of the bootstrap of Hagedorn states respecting the conserved quantum numbers baryon number B, strangeness S, isospin I is implememted into the GiBUU transport model. Using a strangeness saturation suppression factor suitable for nucleon-nucleon-collisions, recent experimental data for the strangeness production by the HADES collaboration in Au+Au and Ar+KCl is reasonable well described. The experimental observed exponential slopes of the energy distributions are nicely reproduced. Thus, a dynamical model using Hagedorn resonance states, supplemented by a strangeness saturation suppression factor, is able to explain essential features (multiplicities, exponential slope) of experimental data for strangeness production in nucleus-nucleus collisions close to threshold.