The short answer is, nothing. Earthquakes don't originate at the earth's inner or outer core, they originate much closer to the surface, usually when there is movement between two or more sections of the earth's crust along breaking lines called "faults". Sometimes the pieces of crust, called "plates", can move laterally past each other along a strike-slip type of fault, which is what happened in Haiti. Earthquakes can also occur when a plate, is subducted underneath another plate, or when two plates are pushed against each other and neither one is subducted.

All of these movements generate seismic waves which travel through the earth. Two main types of waves are produced from these events, P-waves (primary waves) and S-waves (secondary or shear waves). Geologists can measure the intensity of these waves as they reach their destination point. P-waves will penetrate and travel through the earth's core, but are refracted or bent somewhat, and S-waves will not penetrate the core. Since S-waves cannot travel through liquids, this is one of the reasons that geologists believe the outer core is liquid metal, probably iron and a small amount of nickel. In getting back to your question, there is no known effects of seismic waves causing any sort of disruption to the earth's core. Rather, the earth's core does something to the seismic waves. It either refracts or bends them, or absorbs them.

The nature of earth's core has been an interesting subject with alternative theories put forth by scientists.

According to one theory,

http://www.mb-soft.com/public/tecto7.html
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The opinion that the Core is solid is primarily based on a shadow-effect on earthquake-generated waves. The concept of solid is somewhat a relative term. Very tall mountains are considered solid, even though they have clearly documented very slow flow rates, so, in some sense, those mountains are fluid, and the flow rates have even been measured. Thus, a solid Core can generally be said to be true while still involving relatively slow flow rates. This circumstance would have the effect of acting as solid for the earthquake generated shock waves, but would still allow fluid flow. Such slow flow would cause two additional consequences. First, the very heavy elements could migrate even more centrally, to the Inner Core, including the primary sources of long-term natural radioactivity (such as Uranium). This new perspective puts the Earth's primary inner heat source farther toward the middle of the Earth. Second, this situation would certainly drive (rather slow) convective movements in the Core.

This Core convection would probably tend to stir up the very heavy elements in the center of the Core, so the vertical segregation may not be as distinct as it could otherwise be. More importantly, this slow convection would create a variety of randomly oriented convection cells in the Core. These cells would be somewhat dynamic and fluctuating, in various locations and of variable number. Each such cell would effectively generate an electric flow in a circuit, and would thus create a magnetic field. These convectively created magnetic fields would generally NOT be co-axial with the rotation of the Earth itself!

The individual magnetic fields created by the individual convective Core cells would not be easily noticed or measurable from our perspective at the surface of the Earth. The net, measurable Core magnetic field would be a combination of all of these cell-based magnetic fields
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You can find more information from the source mentioned above.

The hollow earth theory which is very fascinating suggests that the core is as a matter of fact just a cavity. You will find detailed explanation on the seismic nature of waves in the following pages by Jan Lemprecht

http://www.hollowplanets.com/journal/Seismic01.asp