Summary
Here is the short answer: When a user is deleted its primary group is also delete, unless that group also contains other users. In this latter case the user is deleted but the group is not.
We can easily verify this ourselves.
Case 1: No other users in primary group of deleted user
First we consider the case where the primary group contains no other users.
Create the paul user:
root@host:~# useradd paul
Check for the paul group using getent:
root@host:~# getent group paul paul:x:1001:
Delete the paul user:
root@host:~# userdel paul
Check for the paul group using getent:
root@host:~# getent group paul root@host:~#
Notice that there is no output from this command. We can also try to delete the paul group ourselves:
root@host:~# groupdel paul groupdel: group 'paul' does not exist
This confirms that the paul group no longer exists.
Case 2: Additional users in primary group of deleted user
Now we will check to see what happens if we try to delete a user whose group contains other users:
root@host:~# useradd user1 root@host:~# useradd user2 root@host:~# usermod -a -G user1 user2 root@host:~# groups user2 user2 : user2 user1 root@host:~# userdel user1 userdel: group user1 not removed because it has other members. root@host:~# groups user2 user2 : user2 user1 root@host:~# getent group user1 user1:x:1002:user2 root@host:~# getent passwd user1 root@host:~# deluser user1 /usr/sbin/deluser: The user `user1' does not exist.
In this case the user1 user is deleted but the user1 group remains.