How can a 16-bit or more processor store a byte in a byte-addressed memory
For a one-byte read to address 0x01, the CPU can read a 16-bit value and discard half of it.

For a one-byte write to address 0x01, if the memory architecture doesn't support that directly, the CPU needs to read the 16-bit value at 0x00, then replace the second byte with 0xCD, then write a 16-bit value to 0x00.