Pion production in proton-nucleus (p+A) collisions outside the kinematical boundary of protonnucleon (p+N) reactions, the so-called cumulative effect, is studied. Restrictions from energymomentum conservation on the energy of pions emitted in the backward direction in the target rest frame are analyzed. It is assumed that the cumulative pions are produced in p+A reactions by heavy baryonic resonances. The baryonic resonances are first created in p+N reactions. Due to successive collisions with nuclear nucleons the masses of these resonances may then increase and, simultaneously, their longitudinal velocities decrease. We also use the Ultra relativistic Quantum Molecular Dynamics model to reveal the key role of successive collisions of baryonic resonances with nuclear nucleons for cumulative pion production in p+A reactions. Further experimental studies of cumulative hadron production in p+A reactions at high collision energies are needed to search for heavy hadron-like objects and investigate their properties. PACS numbers: 25.75.-q, 25.75.Dw, 25.75.Ld