We report a remarkably robust phenomenon in the HCN/HNC molecule where the population of a target state induced by a resonant multiphoton (MP) pi-pulse along a strongly-coupled subset of states can leak to a background state only weakly coupled to this subset. This resonance leaking of population, which may be complete, is due to the overlap of the resonant MP transition to the target state with a resonant MP transition to the background state that includes the target state as an intermediate. We also demonstrate how the population leak can be fully controlled using fields of greater complexity compared to a single pi-pulse, such as two overlapping, phase-adjusted Gaussian pulses. The robustness of resonance leaking in the HCN/HNC molecule suggests that the phenomenon have a significant probability of occurrence in other molecular systems as well. The implications of our findings for the viability of reduced basis set treatments in providing converged ab initio fields and the predictability of these fields in laser-controlled molecular processes are discussed.