In the nonlinear Schrödinger equation with the dissipative perturbation the collision of a fast soliton with a breather, i.e. a bound state of two solutions which is stable in the presence of the perturbation, is considered. It is demonstrated that the collision results in breaking the breather into two solitons. The relative velocity of the “splinters” and the change of the fast soliton parameters are calculated. The same inelastic process is considered under the action of the conservative perturbation of a special form. The inelastic collision of two breathers is investigated too.