In the absence of external forces, the electric field inside a conductor is supposed to go to zero. This is because if any field were to exist, then the charges in the conductor would experience force and continue moving until they cancelled the field. However, is it true that for any system a certain charge distribution always exists which can successfully cancel all electric field? Could it not be the case that no such configuration exists, forcing the surface charges to remain in constant motion? Are you aware of any experimental, physical, or mathematical explanation as to why field should always be cancelled?