On a usual desktop installation, what you see in /etc/shadow is what you get, and the system users generally don't have passwords set. They're not used for interactive logins, so they don't need passwords.
E.g. on the system I looked at, /etc/shadow has this line for sys:
sys:*:19101:0:99999:7:::
That * is where the password hash would be if the user had a password. But * is an invalid password hash, no password will produce it, so there is no password the user could log in with.
Note that if the password hash field was empty, it might allow login without entering a password. With the Linux PAM libraries, this is controlled by the nullok setting to pam_unix.so (man page):
nullok
The default action of this module is to not permit the user access to a service if their official password is blank. The nullok argument overrides this default.
(if it's enabled, and the password is empty, the module doesn't even ask for the password but accepts the login directly.)
If you really wanted, you could set a password for the system in the usual way, but I would suggest reconsidering what you're doing; there's probably a better way. Also note that they may not have a usable shell set either, e.g. on the system I looked, the sys user's shell is set to /usr/sbin/nologin.
sysuser on Debian is a system user that (AFAIK) exists at this point just for legacy reasons, and thus is not supposed to have a usable login (and if you really need to run something as them, you can just usesudo -u sys /bin/bashto get a shell running as that user, but you should never need to do that).