Below picture shows cut DT880 wires connecting to driver shows inside they are copper with white fibers; those fibers are for interior cable flex strength and not electrically conductive. The repair shop who said they couldn't repair the wire/plug apparently saw those white fibers and didn't know what they are.
That kind of wire can be stripped back far enough to then cut off those protruding fibers leaving a suitable length of exposed copper wiring which can be soldered to either a new TRS/TRRS plug, or any other copper wire. Once those white fibers are out of the way even some old TRS/TRRS plug with a pigtail (segment length) of exposed copper wire still attached can be manually joined to that DT880 wire by just twisting matched "+" and "-" wires together and insulating with electrical tape - soldering is
not obligatory.
However, Beyerdynamic seems to use the white wire for it's "+" and red wire for it's "-"
sometimes on the DT880. So before splicing and soldering it's a good idea to check the headphones wiring by examining the plug (if a TRS plug ohm/conductivity meter which color wire goes to the DT880 plug tip and adjacent plug ring, they're "+", and the "-" color wire is the wire going to the plug sleeve, exposed part of plug farthest from plug tip).
O.P. indicates owning 2 DT880. If the one with "wire ripped" is not where the wire exits the ear cup and has sufficient length to strip back to intact wire then the white fibers can then be cut off to leave the copper wire exposed. If cutting out/off the "ripped" section leaves the headphone cable long enough then only need to strip back both good ends of that wire far enough to cut off the white
fibers and join the respective colored wires together - soldered or manually twisted and "+" and "-" patches individually electrically taped.
Patched headphone cable wires' electrically taped are never as pretty as intact ones, but a lot easier than opening up the ear cups and re-wiring intact wires to the drivers inside. On the "ripped" wire even if once remove that segment a length of additional copper wire can be added (soldered or manually twisted) between the 2 remaining good portions (what exits ear cup and what ends in TRS/TRRS plug) - just resulting in 2 electrical taped splices.
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