It comes to mind that the coefficient of restitution (CR) for collision response only models the separating velocity in the normal direction. Thus, for $CR=0$, the separating velocity of two colliding objects is zero along the normal.
However, the collision impulse $j\hat{n}$ creates both linear motion along the normal, and a torque $\vec{r} \times \hat{n}$, for arm $\vec{r}$ from the center of mass (COM). For $CR=0$, the impulse still creates tangential velocity due to the torque. Then, the objects are still separated by rotating away from each other. Does this make sense? the effect is of "sliding against each other instantaneously".