Hello Shojiro,
Since the ROM APIs reside on an area different than Flash memory, it should not be possible to erase them after erasing the flash memory.

From figure 2.2.1 Memory mapping, LPC81x UM.
Other point to have into account is that the APIs residing on boot ROM will not require the flash memory to execute commands and routines, instead, they use pointers to certain areas of the boot ROM space.
For example :
- The IAP (In application Programming API ) used to perform read and write operations to the flash memory , as directed from the user code. Will require to have an specfic location from the bootROM (#define IAP_LOCATION 0x1fff1ff1) and 32 bytes of RAM to perform commands.
- The other APIs ( like Power Profile, I2C-bus ROM API, and USART API ) requiere a pointer to the ROM driver table (located on boot ROM ) to call their respective routines.

From Fig 51. USART driver routines pointer structure.LPC81x UM.
I hope this information helps you.
Best regards, Diego.