How to Replace an Electrical Box During a Remodel
Once the old box is free, pull the existing electrical cable through the opening and feed it into the new replacement box. Installing an “Old Work” box necessitates a clean, precise opening in
Outer casing on wire was cut. Should this be replaced?
So technically, yes, fix it by moving the box over so that the damaged portion of the wire is inside the box enough that you can strip the damaged part for the splice.
Technical note
This reference is intended for preliminary fiber optic splice closure research. Compatibility, splice capacity, sealing class, tray layout, protection sleeves, installation methods, test limits and applicable standards must be verified for the specific project.