MySQL trigger if condition exists

I think you mean to update it back to the OLD password, when the NEW one is not supplied.

DROP TRIGGER IF EXISTS upd_user;

DELIMITER $$

    CREATE TRIGGER upd_user BEFORE UPDATE ON `user`
    FOR EACH ROW BEGIN
      IF (NEW.password IS NULL OR NEW.password = '') THEN
            SET NEW.password = OLD.password;
      ELSE
            SET NEW.password = Password(NEW.Password);
      END IF;
    END$$

DELIMITER ;

However, this means a user can never blank out a password.

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If the password field (already encrypted) is being sent back in the update to mySQL, then it will not be null or blank, and MySQL will attempt to redo the Password() function on it. To detect this, use this code instead

DELIMITER $$

    CREATE TRIGGER upd_user BEFORE UPDATE ON `user`
    FOR EACH ROW BEGIN
      IF (NEW.password IS NULL OR NEW.password = '' OR NEW.password = OLD.password) THEN
            SET NEW.password = OLD.password;
      ELSE
            SET NEW.password = Password(NEW.Password);
      END IF;
    END$$

DELIMITER ;