Unexpected irreversible damage appeared in samples while investigating pulsed S-N switching in YBaCuO thin films. Examination of a scanning electron microscope image of a damaged film containing a defect revealed a step-like motion of the N-zone. Restoration of crack movement dynamics points to the formation of coherent jets. This would mean that cumulative convergence of unknown incompressible media took place. The known model of an edge barrier, when the S-N border, characterized by width λ eff , bounds a semi elliptical N-zone at the film edges, was applied for clarification of the cumulative convergence. In that model, counteracting forces cause a wave-like unstable form of the barrier S-N border, and further current growth increases the amplitude of wave-like distortions of the border. Then, current reconnection separates bulges from the N-zone and induces the appearance of the circular currents with a trapped magnetic flux. Heat release at the places with trapped flux cause an expansion in these locations and coherent jets originate from touch points due to cumulative convergence. We substantiate that specific properties of the S-N border at λ eff , such as high tensile strength, very high flexibility and also incompressibility, are responsible for the appearance of the cumulative effect. Thus, the N-zone propagation into S state begins by motion of the wave-like border. The non-damaging step-like N-zone propagation into the films without defects is clarified. It is concluded that both the critical current and the damage current are determined by the same barrier with the unstable S-N border, and, therefore, the irreversible damage of the films comes quickly after the current reaches the critical value.