The problem of stability robustness with respect to external inputs is analyzed for passive and strict passive systems, whose storage and supply rate functions are sign-definite with respect to a set containing all compact and globally attracting invariant subsets of the unforced system. The results are obtained using the framework of input-to-state stability and integral input-to-state stability for multistable systems. Several conditions are proposed and the cases when an output stabilizing feedback is needed are highlighted. An application of the obtained conditions is illustrated on the model of multispecies populations.