Over the winter, my dog chewed through the power cord on an a/c window unit. I was going to just add a new plug as the cord is still long enough. I sliced into the wire and found 3 wires (ground, neutral, and hot) and wire braided throughout the cord. I assume this is part of the ground-fault protection, but I don't know how it affects rewiring it. I attempted to open the existing plug to investigate, but it's molded plastic and I haven't been able to get into it. Do I have to use a ground-fault plug or can I just use the 3 wires and wire in a new 3 prong plug? Thanks in advance.
I would assume the braid is just for strength. Ground fault relies on detecting current leaks between hot and neutral.
However, if the existing plug is a GFCI plug, then it is advisable to replace it with a comparable part. Alternatively, you could replace the outlet with a GFCI outlet, or even a GFCI breaker. This would provide the same level of protection with a standard plug.
Some air conditioner units are fitted with a type of plug known as a Leakage Current Detector Interruptor (LCDI) plug which uses that braid to pick up on leakage caused by damaged cords -- this is used for fire safety reasons.
Unfortunately, I don't know of any way to fit replacement LCDIs to damaged appliance cords.