A lot of datasheets I've seen for parts containing EEPROM units specifiy that the device will still function after the EEPROM wears out and will hold the last value programmed.

For instance, the datasheet for the DS1669 digital potentiometer with non-voltaile EEPROM states:

The EEPROM memory cells are specified to accept greater than 80,000 writes before a wear-out condition. If the EEPROM memory cells do reach a wear-out condition, the Dallastat will still function properly while power is applied. However, on power-up the device’s wiper position will be that of the position last recorded before memory cell wear-out.