Some very old necklaces might be strung on string or waxed cord. Because of the movement of the beads on the string, the string can become worn, thin and break. Often, such a necklace would have to be restrung.
Most silver beads are strung on chain or foxtail and sometimes snake chain. It is a matter of personal preference of the artist.
Chain has a very open weave (light density), making it very easy to add a jump ring or fastener on the end. It is often used to string Navajo Pearls.
Foxtail, sometimes called wheat chain, has a medium density yet loose weave. This makes it possible to organize the ends and attach a ring or finisher. And it also results in a stronger, smoother track for the beads to slide on.
For instructions on how to string with foxtail and finish the ends see the photo below and also see the tips on RioGrande
Snake chain which has a very tight weave is sometimes used for stringing sterling silver beads but because of the added step of clamping to finish the ends, foxtail is usually preferred over snake.