  In this paper we show that Dirichlet heat kernel estimates for a class of
(not necessarily symmetric) Markov processes are stable under non-local
Feynman-Kac perturbations. This class of processes includes, among others,
(reflected) symmetric stable-like processes on closed $d$-sets in $\bR^d$,
killed symmetric stable processes, censored stable processes in $C^{1, 1}$ open
sets as well as stable processes with drifts in bounded $C^{1, 1}$ open sets.
