First, before I get answers containing information that I already know, yes, I'm aware that the superuser can reset passwords, and yes, I know that the superuser can log in as other users without knowing their passwords.
I also know it's possible to crack an encrypted password with special programs. I'm talking about directly gaining the password a user types in, as plain text, without the need to decrypt anything.
Of course, a general keylogging program can do this, I assume, but there would be a lot of junk in the output that was not related to passwords, and it may even have safety features built in to prevent this use.
Is it possible for root to put a keylogging program on a machine, that is activated specifically when a user changes their password, and "intercepts" the information before it gets encrypted? It could then send this information to a secret file in root's home directory.