Single I2C EEPROM 24C02 uses all eight addresses by itself
Got exactly the same behavior on eeprom modules from Banggood. 
The chips are marked ATMEL719 24C02N PU27 D

24C04 parts, also from Banggood, works normally.

Chips marked ATMEL178 24C256 PU27 D are also strange. They respond to two addresses (i.e. 57 and 5f) and all 3 address select pins will modify the i2c address pair (i.e. 50 to 57 and 58 to 5f). 

The genuine chip has just one active address and only use the A0 and A1 pins, according to the data sheet.

Caveat Emptor