Consider the following analogy where the beam relates to the box, the cable to the pole and the weight to the vaulter.
Situation 1) A steel cable is secured to an overhead beam. A solid weight is secured to the free end of the cable. The weight is held up so there is slack in the cable. This provides potential energy. The weight is then dropped (converting the potential energy into kinetic energy), the cable doesn't break and the weight bounces slightly and becomes stationary at the end of the cable. So what happens in this case is the weight is entirely rigid and therefore doesn't stretch and convert kinetic back to potential energy. The beam is very rigid and doesn't doesn't stretch and convert kinetic back to potential energy. The cable, although very strong likely stretched somewhat and converted most of the kinetic energy to potential and then returned it when it rebounded to its origianal length.
Situation 2) Now instead of a solid weight, an automotive innertube is filled with water and secured to the end of the cable. When this "weight" is dropped and it reaches the end of the cable, the inner tube is likely stretched and is what converts and returns almost all of the energy. (Hopefully it was a strong tube and didn't "pull a muscle".)
Situation 3) We keep the solid beam and the inner tube but replace the steel cable with a "bridge jumping" bungie. We drop the weight. The beam continues it's role. The bungie resists the inner tube but yields and stretches. The bungie is strong enough that it doesn't yield without a fight and the inner tube stretches in response. When each of these two elements stretch, they are converting kinetic energy back into potential energy. This is at a maximum when the bungie and the inner tube are at their maximum stretch.
A person can imagine each of these components having a degree of variability. The box (the beam) could be mounted in concrete or it could be a sliding box. The pole (the cable) could be made of steel or fiberglass. Our bodies (the weight) have some range of ability to stretch and rebound without damage, but this is minimal. However, how and when we move our bodies does impact the effective "flexibility" and efficiency of this compenent. Depending on the combination, each component will convert various amounts of the kinetic energy of the run.
Another important part of the discussion is the efficiency of the flexible parts of the system. If these are perfect components, no energy is lost. But they aren't. (If this were possible you could create a perpetual motion machine.) The lost energy is usually given up as heat from internal friction or external (with the air) friction. Modern poles I believe are very efficient, meaning most of what you put in you get back out. Using it efficiently (transferring the run kinetic energy into bending the pole and being positioned to use that energy when it unbends) is what makes vaulting a competitive sport.
- master
PS I modified this post, removing the word absorb and replacing it with what I think to be a more correct description.