Doesn't matter what the storage is, you aren't storing the password
Of course you are storing the password. your not storing it in plaintext, or anything you would be able to read it from, but you are still storing it somewhere, if you weren't then you would have nothing to compare the input to when they tried to log in. (password encryption essentially works by making sure that searching for an answer takes much longer than checking it (N=NP style) but you DO still have to check it against something. if you didn't either any password would work or none would).
As pointed out by another person who replied to me however, you need to set the standard size to properly hash a password, which gives you a standard filesize for all of them regardless, so setting an unlimited password length while properly hashing it is impossible using standard methods.
Also your math is waaay off. A 2 character password doesn't have 236 (~69 billion) combinations with only letters and lowercase numbers... I'm not sure you know how passwords or permutations work.
Yes I do. the number of possible permutations for any set of data is the number of states to the power of the number of iterations.
Which is why my comment was incorrect, it would be 3620 not 2036. I am at work so I didn't have time to double check that, my bad.
So a 2 bit password has 362 or 1296 possible combinations, and a 20 character password has 3620 or 13367494538843734067838845976576 possible permutations rather than the previously stated 2036 or 68719476736000000000000000000000000000000000000. still more possible states than is reasonable for anything to guess randomly, so the overall point stands.