In skidding the drivetrain is stationary, therefore the only forces on the chain are shear. Think of a moving drivetrain like pushing a piece of wood into a saw. The rotation creates (in a saw's case) huge erosion. Now try pushing the same piece of wood into a stationary wood. Nada. There will be some elastic deformation, but nothing plastic. (permanent) Besides, the force of skidding in-progress is smaller than the force of starting from a stop. (static friction of the tires > kinetic friction)