This safety system includes: a toothed wheel, connected rotationally with respect to at least one rotating member to be braked, a worm driven rotationally by a motor upon rotation of the rotating member and permanently in mesh with the toothed wheel, a housing forming: a longitudinal wall located on the side of the worm diametrically opposed to the toothed wheel, and extending along the worm at a distance of the latter ranging between 0.001 and 0.01 times the diameter of the worm, and a first end wall integral with the longitudinal wall, located opposite a first longitudinal end of the worm; and energy absorption/dissipation elements interposed between the first end wall and the first longitudinal end of the worm, the worm being slidingly mounted in the housing such that the first longitudinal end of the worm comes closer to the first end wall when the worm slides in the housing.