Step 1. Put internal EEPROM into the Cortex M3 chip (carefully!)
Hmm yes true, if someone can make an deal with the controller on the programming port as EEPROM.
In all seriousness, the Due has no EEPROM at all. There is the possibility to store things in the FLASH memory but, since it gets totally erased every time you program the Due, this is not ideal. So, really, if you need EEPROM you've got to put it on a shield.
If someone can mod the firmware for sending special commands over uart to let the controller know someone will use the EEPROM from the controller to store or get some data.