It is fairly common to put deliberate break points in rope or cable to ensure that they fail in a controlled and predictable manner when overloaded. Typically this is done in tings like fishing rigs or oil well wire-line winches to try to ensue that any overload condition results in a least bad scenario for example by preventing overload of expensive bits of kit or leaving making disconnected equipment potentially recoverable.
It is often preferred to put in a specific breakaway linkage rather than design it into the rope itself as this makes it simpler to engineer and manage as you can add it to an existing system and change to breakaway characteristic fairly easily and also gives you a predicable point of failure. Plus it potentially saves you from scrapping an expensive length of cable if it does fail as you can be reasonably sure that the cable itself wasn't overloaded.
As well as in-line linkages whcih can be placed anywhere in the system there are also various other systems such as torque limiting clutches and various types of tear failure linkages which are also good at absorbing and mitigating impact forces.
You could also use inertial and/or damping systems to engage or disengage clutches or couplings a bit like an inertial reel seat-belt in reverse.
Perhaps the simplest system is just a shear pin as part of a clevis type coupling . For failure under jerk conditions a brittle material with a notch might be a good option.