This is not a tutorial. Just
documenting an experiment.

The influences can be adjusted for desired effect.
If you also moved the copied bones to a different location in order not to get
confused, snapped them back ontop.
Go ahead and hide all the other bones.
Create a Jaw Bone and an IK bone.
When you move the jaw bone down, we want the corners to move inside. In order
to do that we need to copy the change and apply it to the corner bones.

Add following constraint to those bones.
Notce we added a "local" copy location constraint. What this does is,
it copies the location of IKJaw bone and applies it locally.
Now add a Copy Location constraint to the bones previously created, copying the
location of the bones just created.
here is the blend file demonstrating the result.