Non-metallic materials that are normally non-conductors of electricity can start to conduct whenever their locked-in-place electrons are suddenly allowed to move, or are forced to move.
Nothing can conduct electricity unless it contains electrons (or ions) that are free to move. This is the case for most metals, which are very good electrical conductors. Other materials do not have the free electrons, and so generally they will not conduct, and are classified as insulators. Some are better at either conducting or insulating than others.
Air, for example is a great insulator. That is, until it gets rubbed too hard and too fast. Then air becomes a very powerful but brief conductor of electricity referred to as lightning.
Salts will not conduct electricity at room temperature. But if they are dissolved in water, the solutions will conduct electricity for a while, at least. Here, the electricity is conducted by ions in the solution until they are all used up. Another way to make salt conduct is to melt it, and it will conduct as long as the heat is present.
Semiconductors are the metalloids, halfway between metals and non-metals, and they can be formulated to conduct electricity and to insulate at the same time, to provide us with a huge array of electronic products. All of these conductors need electrons or ions that are free to move.