The Enet-232/4 contains the UARTS, 16MB of SDRAM, and 2MB flash. The UARTS and SDRAM are volatile. There are other buffers located in the processor and network layers, but these are also volatile like the SDRAM and UART buffers.
The flash contains an image of the embedded operating system. Other information such as serial number and MAC address are also stored there. However no serial data is stored in the flash.