  In this paper, we give a complete characterization on which finitely
generated subgroups of finitely generated $3$-manifold groups are separable.
Our characterization generalizes Liu's spirality character on $\pi_1$-injective
immersed surface subgroups of closed $3$-manifold groups. A consequence of our
characterization is that, for any compact, orientable, irreducible and
$\partial$-irreducible $3$-manifold $M$ with nontrivial torus decomposition,
$\pi_1(M)$ is LERF if and only if for any two adjacent pieces in the torus
decomposition of $M$, at least one of them has a boundary component with genus
at least $2$.
