I am sorry, it is not possible to get a replacement for that cable. And, Google does not have an option to repair it.
Since the 2nd Gen hasn't been sold since late 2018 you are well out of warranty.
Your only option is to buy a replacement device.
The newer Chromecast with Google TV models are quite a step up. They now include a remote and an interface so you can use apps directly on the Chromecast and not rely on your phone or tablet to cast. They also have upgraded processors and wifi radios in them.
