Let $V$ be a simple $C_2$-cofinite VOA of CFT-type and we assume
$\Hom_V(U\boxtimes V',V)\not=0$ for some $V$-module $U$, where $V'$ is the
restricted dual of $V$. We prove that every $V$-module $W$ is semirigid, that
is, for any epimorphism $e_W:\widetilde{W}\boxtimes W\to V$ and a canonical
isomorphism $\mu:(W\boxtimes \widetilde{W})\boxtimes W \to W\boxtimes
(\widetilde{W}\boxtimes W)$, there are homomorphisms
$e_{\widetilde{W}}:W\boxtimes \widetilde{W}\to V$ and $\rho:P \to W\boxtimes
\widetilde{W}$ such that $e_{\widetilde{W}}\rho(P)=V$ and $({\rm id}_W\boxtimes
e_W)(\mu(\rho\boxtimes {\rm id}_W)(P\boxtimes W))=W\boxtimes V$, where $P$ is a
projective cover of $V$. As a corollary, we have that $W$ is flat for the
fusion products $\boxtimes$, that is, $0\to W\boxtimes A\to W\boxtimes B \to
W\boxtimes C\to 0$ is still exact for any exact sequence $0\to A\to B\to C\to
0$ of $V$-modules.