If they hash a subset, then those extra characters are literally irrelevant, since the hash algorithm will exclude them. Like if they just hashed the first 5 characters, then “passw” is the same as “password” and all those permutations. Hashing is safe because it’s one-way, but simple testing on the hashing algorithm would reveal certain characters don’t matter.
Protecting a smaller subset of characters in addition to the whole password is slightly better but still awful. Cracking the smaller subset will be significantly easier using rainbow tables, and literally gives a hint for the whole password, making a rainbow table attack significantly more efficient. Protecting the whole thing (with no easy hints) is way more secure.
It also adds nothing to keylogging, since it’s not even a new code, it’s part of the password.
There was a time where that level of security was acceptable, and it still could be ok on a closed system like an ATM, as the other reply to my comment pointed out, but this kind of protection on a standard computer is outdated and adds holes.