Most of the energy goes into a number of places. Bouncing around after the fall, elongating the spring of the rope, permanetly deformation of the core of the rope, and the friction between the rope and the carabiners/rock (especially the carabiner that is actually catching you).

Let's say for one moment we look at the top most carabiner. Let's assume that you hit 8kN of force during a decent fall and the sliding coefficient of friction for the rope's sheath and the aluminium is .2.

At this moment, that carabiner would be resisting with 1.6 kN of force. This is equal to a 360 lbs of dampaning force. This is why you do not bounce a LOT when you fall on a climbing rope. There is a ton of friction in your system.

The internal friction in the rope itself absorbs very little of the actual energy of a fall.