Consider a ball formed with a plastic outer surface surrounding a metal ball in its inner core. Will the plastic outer surface accumulate and retain a static electric charge (of electrons) when rubbed with fur/flannel/silk? Or, will the electrons flow from the surface of the ball and disappear into the inner iron ball?
Answer: Yes, the plastic outer surface will accumulate and retain a static electric charge because plastic is an insulator, and the electrons accumulated on the surface of the plastic sphere cannot flow through the insulator to the inner metallic core, nor can they flow on the surface of the insulator to distribute themselves to a lower energy configuration.
No, the negative charges will not disappear internally into the metallic ball in its center, again because the plastic is an insulator and will not allow flow below the breakdown voltage. There is an attraction between the surface electrons and the metallic center ball. The surface charges emit an $E$ field, which polarizes the metallic core. That is, the conduction electrons in the metal ball are repelled by the surface electrons, which causes the conduction electrons in the metal ball to move to the opposite side of the metal ball. This, in turn, leaves the near side of the metal ball with a positive charge. Thus, the electrons on the surface of the plastic are attracted to the positively charged region. But again, since the electron accumulation is on the surface of an insulator, those charges cannot flow through the bulk of the plastic insulator to neutralize that induced positively charged area on the metal ball.
Elaboration: When two insulators (with different electron affinities) are touched/rubbed (e.g., plastic and wool), electrons accumulate on the surface of the material with the greater electron affinity. A plastic ball has a greater affinity for electrons than fur.
Static Shock - touching a doorknob: Consider the static electricity accumulation after walking across a carpet in a dry environment, and upon touching a metal doorknob, you receive a shock. Walking with rubber shoes on a nylon carpet causes electrons to accumulate on the soles of your shoes. The electrons accumulated on your shoes probably don't flow up to your hand, and then onto the doorknob. Rather, since rubber is an insulator, the electrons accumulated on your shoes probably polarize your body like the plates of a capacitor charge a dielectric. So, when you touch a metal object, such as a doorknob, the static charge (extra electrons) on your hand induces the opposite charge in the metal of the doorknob. (That is, the electrons on your hands repel the electrons in the metal, thereby inducing a positive charge in the metal of the doorknob metal close to your hand - the electrons are repelled far away, on the other side of the doorknob.) The extra electrons on your hand jump to the electron-deficient metal (which you created, just before you touched it). If the voltage is sufficiently high, the air ionizes, creating a plasma channel for the electrons to flow across. The flow of current stimulates your nerves, giving the sensation of being shocked. The current stops flowing from your hand when the field from the charges accumulated on the metal doorknob equals the field from the charge on your hand.
This example is relevant because this same phenomenon is what happens with the plastic ball with the steel inner sphere. The static charge on the surface will conduct to the steel ball in the center, but only if the voltage is high enough to exceed the breakdown voltage of the plastic. In general, a voltage of not more than a 20,000 volts will generate by rubbing fur and plastic, which will probably be insufficient.
Plastic is an insulator, and when rubbed by fur (or any other material with less electron-affinity than plastic), electrons accumulate on the surface of the plastic. Of course, the fur, the source of the electrons, is now electron-deficient and positively charged. But, because plastic is an insulator, the captured electrons on the surface of the plastic are immobile. Electrons can, and will, redistribute themselves over the surface of a metal. These static-electricity electrons remain in place forever unless removed or neutralized, for example by the water molecules in humid air. See Example
Summary: In the case of a plastic ball with an internal metal sphere, the ball's plastic surface will accumulate electrons when rubbed by fur (etc.). The captured electrons stay in the spot where they were captured. The electric field generated by the electrons accumulated on the plastic's surface polarizes the inner metallic ball (electrons are repelled to the far side of the ball, leaving an area of positive charge on the near side). The oppositely charged regions (negative charges on the plastic and positive charges on the near-side of the metal ball) attract each other. But, the because the plastic is an insulator, the electrons on the plastic's surface are unable to flow through the bulk of the plastic to neutralize the volume of positive charge induced in the metal ball.