Electrons move when a field acts on them. If the electrons move towards the field, they cancel out the field when enough electrons build up.
Shouldn't the free electrons stop moving eventually and reach a stable system where there is no field acting on any electron? I would expect them to keep moving until they build up to cancel out the field acting on other electrons resulting in the system being static. Please don't make your answers too technical, I don't know a lot about physics.
EDIT: I have no knowledge of quantum mechanics but I believe the random motion I'm talking about is called the Fermi velocity.