The production of backward nucleons, $N(180^\circ)$, at $180^\circ $ in the nuclear target rest frame in proton-nucleus (p~+~$A$) collisions is studied. The backward nucleons appearing outside of the kinematically allowed range of proton-nucleon (p~+~$N$) reactions are shown to be due to secondary reactions of heavy baryonic resonances produced inside the nucleus. Baryonic resonances $R$ created in primary p~+~$N$ reactions can change their masses and momenta due to successive collisions $R+N\rightarrow R +N $ with other nuclear nucleons. Two distinct mechanisms and kinematic restrictions are studied: the reaction $R+N\rightarrow N(180^\circ)+N$ and the resonance decay $R\rightarrow N(180^\circ) +\pi$. Simulations of p~+~$A$ collisions using the Ultra-relativistic Quantum Molecular Dynamics model support these mechanisms and are consistent with available data on proton backward production.