This phenomenon is referred to as electrostatic shielding. $\vec E_{net}$ = $0$ when there are no charges placed inside the volume of the closed conductor irrespective of whether there is an external $\vec E$ surrounding the conductor.
Say there is an electric field $\vec E_1$ from left to right outside the conductor. The electrons on the surface of the conductor will then align themselves such that the surface closer to the direction of $\vec E$ will be relatively negatively charged and the surface further from the direction of $\vec E$ will be positively charged. This creates an equal and opposite $\vec E_2$ within the conductor, thus cancelling out the external field and making $\vec E_{net} = 0$ within the conductor. Hope this helps.
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