In traditional pearl bead stringing, pearls are strung on silk bead cord. This is still true today for any type of high end pearl necklace, and there are a couple of reasons why.
One reason is that both pearls and silk are natural in origin, and therefore complement each other, and also both have a value to them. Silk also picks up the soft sheen of the pearl luster, and makes a necklace made this way flow in style and look.
However, the main reason that pearl necklaces are strung on silk bead cord is because of safety. Pearls strung on silk bead cord are strung one at a time, then a knot is tied in the bead cord between each individual pearl. Necklaces and bracelets strung this way most often also have a safety clasp, and might also include a safety chain too. These are all ways of preserving the pearls if the necklace should be broken at any point along the strand.