  We investigate long-time behaviors of empirical measures associated with
subordinated Dirichlet diffusion processes on a compact Riemannian manifold $M$
with boundary $\partial M$ to some reference measure, under the quadratic
Wasserstein distance. For any initial distribution not concentrated on
$\partial M$, we obtain the rate of convergence and even the precise limit for
the conditional expectation of the quadratic Wasserstein distance conditioned
on the process killed upon exiting $M\setminus\partial M$. In particular, the
results coincide with the recent ones proved by F.-Y. Wang in \cite{eW2} for
Dirichlet diffusion processes.
