This is a separate code to your password, and there is no reason each letter could not also be stored as a hash after being salted with some personal information.
> there is no reason each letter could not also be stored as a hash after being salted with some personal information.
There's no technical reason, but you may as well just store it as plain text.
Even assuming everyone used all the available Unicode symbols (~110,000 according to Wikipedia) an eight character password would only require calculating 880,000 hashes in order to brute force every character.
Assuming a more realistic A-Za-z0-9, an eight character password is an absolutely pathetic 496 hashes. A 1,024 character password (good luck remembering that) is still a paltry 63,488.
For comparison, hashed as a whole that same A-Za-z0-9 at eight characters is 218,340,105,584,896 (62^8).
Hashing the characters individually changes adding more characters from exponentially increasing the work involved to linearly. It's good as useless.