The correct set-up would be "What would happen if an immovable object were confronted with an unstoppable force." We will have to further define out unstoppable force as having infinite momemtum (right?) and the immovable object having infinite inertia (right.) Therefore, our unstoppable force would have an infinite energy (measure this in joules/calories/whatever) and the unstoppable force would be able to absorb infinite energy.

There would be an endless transfer of energy.

The two would appear as if they are resting, but are actually transferring their infinite energies from one to the other. Equilibrium or a relation would never be establieshed since we're dealing in the infinite regarding energy.

Sad, but true