If the users are part of an Enterprise domain (i.e. synched from LDAP), then the password is not stored in the LiveCycle (user manager) database, the password is managed by the LDAP server. There is not interface from LiveCycle to change the password stored as part of their LDAP account.
If the users are part of a local domain, the "Administrator" can change a users password manually. I am not aware of any "out of the box" way for users to change their own password, nor do I believe this functionality exists in the APIs
Regards
Steve