I am not exactly sure I understand your question, but if I understand
correctly the wire broke off near the terminal screw at a switch.

If that is true, the weakness could be caused by someone using
strippers incorrectly. If they used the wrong size hole in wire
stripers this can cause a weakness.

i have a 100% solution for broken wires where the box is too small and the wires too short. install new wiring and abandon the original box, thats what blank covers are for

sometimes its just easier.