Three strand twisted line can be "laid" right or left, and should always be coiled with the lay of the line. This rope is described as S-laid (left-laid) or Z-laid (right-laid) according to whether the twist follows the line of the center part of the letter S or Z. Most three strand rope is Z-laid (right-laid) If you hold a length of 3 strand right-hand laid twisted line at arm's length and eyeball it, you will see the wrap of the line twisting to the right.
8-strand Multiplaited (“Brait”, “Octoplait”, etc) is braided with 2 pairs of Z-laid and two pairs of S-laid strands – it is flexible and does not kink.
Proper “Fall Arrest” safety lines must be elastic (stretchy) to prevent severe injury. This is not practicable on sailboats where we use relatively inelastic halyards for the purpose. As Auzzee (David) notes, this is why it is imperative that the deck crew maintain the tag line tight, so that there is little/no slack (hence no appreciable fall).