This paper deals with human-cable collision detection with a Cable-Driven Parallel Robot (CDPR) and a control strategy to safely release the tension in the cable in contact with a human operator. The main purpose of this work is to contribute to the development of safety solutions allowing collaborative work between human and robot with CDPRs in production tasks. Using a geometric model of cable deformations under an external collision, a direct relationship is established between the initial cable tension, the collision force and the increase in cable tension. This relationship is validated experimentally with an ad-hoc test bench. Collision force levels are set to admissible values in order to prevent harm for human operators. A collision detection is then implemented on the 8-cable suspended CDPR CRAFT prototype using this method, continuously comparing the cable tensions measured by sensors with admissible cable tension increases. Using these results, an approach aiming at releasing a collided cable so as to minimize risks for operators and the environment of the robot is proposed with an adaptive control scheme, based on a progressive cable tension management once a collision is detected. This cable tension management is simulated and represented in the null space of CDPR wrench matrix. Feasibility domain of this tension management and alternative solutions outside of it are also discussed. This work contributes to the safety of collaborative CDPRs by determining a direct relationship between collision force and cable tensions in the event of a collision and by introducing a collision detection method.