A safety device is provided having a clamping system that uses pressure admission into a chamber of a clamp element dependent on the position of a weight to be carried relative to the clamping system. For this purpose a valve is provided in a medium supply line, which valve is to be opened or closed by means of a movable actuation element. Here, the actuation element should be movable in the same direction in which the weight moves, preferably in a vertical direction. As a result of the arrangement of such a valve, the device couples the vertical movement or position of the weight with an actuation of the valve, and thus to provide an additional control for the pressure admission into the chamber or the clamping force resulting therefrom. A preferred chamber has curved top and bottom walls that elongate with a pressure drop.