I searched 4512a2zli and found a datasheet, replacing it won't do you any good, it's a 512k EEPROM, so it's the data on it that's important, not the chip itself.
If this portion is actually broken, your best bet is probably to locate a replacement module. The piece of board with castellations is undoubtably an off the shelf module of some description, even if it's hard to get your hands on, rather than a circuit specific to the headphones, so I'd just locate a replacement module and replace the whole thing.
That said, it's not a terribly likely thing to fail, so I would try to exhaust other options first.