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I am trying to login to Debian 9 machine with root username,
locally and through ssh. 
It logs in with any invalid password. 
I want to access the machine with the correct password only. 
Why does an invalid password for the root account work? 
How do I fix it so correct password entry is required, locally and through ssh?

For ssh I allowed only the root user. 
Interestingly, when I change UsePAM to no, it works with correct root password.

ssh debug result:

OpenSSH_7.9p1 Debian-1, OpenSSL 1.1.1  11 Sep 2018

debug1: Reading configuration data /etc/ssh/ssh_config

debug1: /etc/ssh/ssh_config line 19: Applying options for *

debug1: Connecting to 192.168.56.101 [192.168.56.101] port 22.

debug1: Connection established.

debug1: identity file /root/.ssh/id_rsa type -1

debug1: identity file /root/.ssh/id_rsa-cert type -1

debug1: identity file /root/.ssh/id_dsa type -1

debug1: identity file /root/.ssh/id_dsa-cert type -1

debug1: identity file /root/.ssh/id_ecdsa type -1

debug1: identity file /root/.ssh/id_ecdsa-cert type -1

debug1: identity file /root/.ssh/id_ed25519 type -1

debug1: identity file /root/.ssh/id_ed25519-cert type -1

debug1: identity file /root/.ssh/id_xmss type -1

debug1: identity file /root/.ssh/id_xmss-cert type -1

debug1: Local version string SSH-2.0-OpenSSH_7.9p1 Debian-1

debug1: Remote protocol version 2.0, remote software version OpenSSH_7.4p1 Debian-10+deb9u4

debug1: match: OpenSSH_7.4p1 Debian-10+deb9u4 pat OpenSSH_7.0*,OpenSSH_7.1*,OpenSSH_7.2*,OpenSSH_7.3*,OpenSSH_7.4*,OpenSSH_7.5*,OpenSSH_7.6*,OpenSSH_7.7* compat 0x04000002

debug1: Authenticating to localhost:22 as 'root'

debug1: SSH2_MSG_KEXINIT sent

debug1: SSH2_MSG_KEXINIT received

debug1: kex: algorithm: curve25519-sha256

debug1: kex: host key algorithm: ecdsa-sha2-nistp256

debug1: kex: server->client cipher: chacha20-poly1305@openssh.com MAC: <implicit> compression: none

debug1: kex: client->server cipher: chacha20-poly1305@openssh.com MAC: <implicit> compression: none

debug1: expecting SSH2_MSG_KEX_ECDH_REPLY

debug1: Server host key: ecdsa-sha2-nistp256 SHA256:>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

debug1: Host 'localhost' is known and matches the ECDSA host key.

debug1: Found key in /root/.ssh/known_hosts:3

debug1: rekey after 134217728 blocks

debug1: SSH2_MSG_NEWKEYS sent

debug1: expecting SSH2_MSG_NEWKEYS

debug1: SSH2_MSG_NEWKEYS received

debug1: rekey after 134217728 blocks

debug1: Will attempt key: /root/.ssh/id_rsa 

debug1: Will attempt key: /root/.ssh/id_dsa 

debug1: Will attempt key: /root/.ssh/id_ecdsa 

debug1: Will attempt key: /root/.ssh/id_ed25519 

debug1: Will attempt key: /root/.ssh/id_xmss 

debug1: SSH2_MSG_EXT_INFO received

debug1: kex_input_ext_info: server-sig-algs=<ssh-ed25519,ssh-rsa,ssh-dss,ecdsa-sha2-nistp256,ecdsa-sha2-nistp384,ecdsa-sha2-nistp521>

debug1: SSH2_MSG_SERVICE_ACCEPT received

debug1: Authentications that can continue: publickey,password

debug1: Next authentication method: publickey

debug1: Trying private key: /root/.ssh/id_rsa

debug1: Trying private key: /root/.ssh/id_dsa

debug1: Trying private key: /root/.ssh/id_ecdsa

debug1: Trying private key: /root/.ssh/id_ed25519

debug1: Trying private key: /root/.ssh/id_xmss

debug1: Next authentication method: password

debug1: Authentication succeeded (password).

Authenticated to localhost ([localhost]:22).

debug1: channel 0: new [client-session]

debug1: Requesting no-more-sessions@openssh.com

debug1: Entering interactive session.

debug1: pledge: network

debug1: client_input_global_request: rtype hostkeys-00@openssh.com want_reply 0

debug1: Sending environment.

debug1: Sending env LANG = en_US.UTF-8

debug1: client_input_channel_req: channel 0 rtype exit-status reply 0

debug1: client_input_channel_req: channel 0 rtype eow@openssh.com reply 0

debug1: channel 0: free: client-session, nchannels 1

debug1: fd 2 clearing O_NONBLOCK

Connection to localhost closed.

Transferred: sent 2356, received 6188 bytes, in 7.3 seconds

Bytes per second: sent 321.4, received 844.0

debug1: Exit status 0

I solved it. PAM contains different files and one of the files common-auth was mis-configured. There was deny status on any invalid login, so I changed it and the problem solved.