Cable-Driven Parallel Robots (CDPRs) have been little used so far for collaborative tasks with humans. One reason is the lack of solutions to guarantee the safety of the operators in case of failure. Therefore, this paper aims to determine the possible failures of CDPRs when they are used for collaborative work with humans and to provide technical solutions to ensure the safety of the operators. A translational three degrees-of-freedom CDPR composed of four cables connected to a point-mass end-effector is considered as an illustrative example. The cables are supposed to be ideal, namely, they are not elastic and do not exhibit sagging.