Conductors and Insulators

Yes, an insulator can begin to conduct electricity under highly extreme conditions. Too strong of an external electric field can be applied across an insulator, which can let it pull electrons away from their atoms. That frees them to conduct electricity. This phenomenon is known as dielectric breakdown.

Distilled water is one of the best examples of an electrical insulator. Very few ions are free and they are not enough to carry charge. But, if you look at tapwater or saltwater, it can be an effective conductor, as these liquids have dissolved salts and minerals acting as mobile charge carriers. They allow electricity to flow. 

The conductor needs to be in electrostatic equilibrium for the electrostatic field to become zero inside it. Any conductor will have electrons or electric charges that are moving freely inside the substance. When you apply an external electric field, these free electrons will redistribute until the time the internal field they create begins to cancel out the external field. That's why the total or net electric field inside the conductor becomes zero. 

The best conductor of electricity is Silver (Ag) at room temperature. It is not used in normal wiring even though being the best conductor because of its high cost.

• Electrical Conductivity ($\sigma$): $6.3 \times 10^ {7} \ \text {S/m}$

• Electrical Resistivity ($\rho$): $1.59 \times 10^ {-8} \ \Omega \cdot \text {m}$ (the lowest among all metals)