This is a problem of energy conservation: the cue ball starts with E = 1/2 mv^2 kinetic energy and, no matter what, that same amount of energy has to exist afte

This is a problem of energy conservation: the cue ball starts with E = 1/2 mv^2 kinetic energy and, no matter what, that same amount of energy has to exist afterwards in some form. But where will it go? In an elastic collision, a negligible amount of energy gets converted to heat (through inelastic deformation), and only a small amount will be converted to sound. The only other place the energy can go is kinetic energy distributed between the balls. This means that there's no way to cause the balls to collide such that they're stationary afterwards. Hypothetically, you might be able to completely convert the linear motion into rotational motion and have the balls spinning on the spot afterwards... but that's about it.