It's pretty hard to give you specific instructions without actually seeing the shot. My first impulse would be to Motion Stabilize the shot first so the face does not move. Then add an adjustment layer and a null. Attach the Motion Stabilized face layer's Anchor Point to the Null's position property using an expression and then parent the Face layer to the null. This will put the motion back in the shot and give you some data you can use for the Distortion Mesh offset Now add an adjustment layer and distortion mesh. Tie the Distortion Mesh Offset to the position of the null using an expression generated with the pickwhip. Now use the liquify effect tools to distort the face. When the face moves the distortion will stick to the face. Imagine that the green layer with the grid is the face layer:

That's everything you should need to do to stick the Liquify effect to a face.
On the other hand, if the face is turning or something else is going on in the shot an entirely different approach may be called for. Show us the shot and I can give you a better idea of how to do the shot.