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You write the read value directly to value, while value is actually and array. Try this instead.

void loop() {
    value[0] = EEPROM.read(address);
    value[1] = EEPROM.read(address + 1);
    Serial.print(address);
    Serial.print("\t");
    Serial.print(value[0]);
    Serial.print("\t");
    Serial.print(value[1]);
    Serial.println();
    address = address + 2;

    if (address == 512) {
        address = 0;
    } // not address==0;

    delay(500);
}