A methodology to obtain the minimum weight of cables in cable-stayed bridges when a cable fails has been developed. To this end, a multi-model strategy is proposed that takes into account design constraints in both the intact and damaged models. The dynamic effect of the cable breakage is considered by the application of impact loads at the tower and deck anchorages. The methodology is applied to the Queensferry Crossing Bridge, a multi-span cable-stayed bridge with cross stay cables in the central section of each main span. The number of cables, anchorage position on the deck, cable areas and prestressing forces are considered as design variables into the optimization process simultaneously. The fail-safe optimum design results in a different cable layout than the optimized design of the intact structure, with minimum volume increase.