  Extending a previous work by the same authors, we investigate the existence
of expansion-free dynamical stars with non-zero spatial twist and rotation and
show that such stars cannot exist. Firstly, it is shown that a rotating
expansion-free dynamical star with zero twist cannot exist. This is due to the
fact that such stars cannot radiate and they are shear-free, in which case the
energy density $\rho$ is time independent. Secondly, we prove that a
non-rotating expansion-free dynamical star with non-zero spatial twist also
cannot exist, as either the strong energy condition must be violated, i.e.
$\rho+3p<0$, or the star must be shear-free in which case the star is static
($\Theta=\Omega=\Sigma=0$). Finally, if we insist that the rotation and spatial
twist are simultaneously non-zero, then the star cannot be shear-free in which
case we obtain a quadratic polynomial equation in $\phi$ and $\Sigma$ with no
real solutions. Therefore such stars cannot exist.
