The phenomenon of destruction of silica fiber cladding by the fiber fuse effect has been observed for the first time to the authors' knowledge. Experiments on the optical discharge propagation along a fiber were conducted with fibers of decreased cladding thickness. The destruction of fiber cladding led to expansion of the optical discharge plasma and to a decrease of its density. This resulted in the termination of optical discharge propagation. The section of a fiber with decreased cladding thickness can act as a safety device to halt damage propagation.