The breaking of a plane self-excited dust-acoustic soliton in a dust cloud formed in stratified dc glow discharge plasma is studied. Both macroscopic and kinetic parameters of the dust component near the soliton are experimentally obtained. It is shown that the breaking of a soliton can accelerate charged particles to supersonic speeds. The theoretical interpretation of the experimental results is performed in the framework of the hydrodynamic plasma approach, as well as the single-particle approximation. Both dissipative and nondissipative cases are considered.