We theoretically investigate the possibility of the formation of subcycle dissipative solitons propagating in a multilevel resonant medium. We examine the case when the duration of light pulses is significantly smaller than the periods of resonant transitions in the medium. Within such an approximation, a nonlinear integro-differential equation describing the spatiotemporal evolution of the electric field was derived. We demonstrate that in the case of a preexcited medium, this equation has solutions in the form of stable half-cycle unipolar dissipative solitons with the parameters determined by the medium properties. The obtained results can provide an important step towards the efficient transmission of subcycle pulses through optical media.