Yes. The POSIX specification requires the shell to set a value for $HOME:

HOME
The system shall initialize this variable at the time of login to be a pathname of the user's home directory. See pwd.h.

What about user nobody?

# su - nobody
No directory, logging in with HOME=/
$ echo $HOME
/

Even though nobody has no true home, HOME is set to the root directory.

Yes. The POSIX specification requires the OS to set a value for $HOME:

HOME
The system shall initialize this variable at the time of login to be a pathname of the user's home directory. See pwd.h.

What about user nobody?

# su - nobody
No directory, logging in with HOME=/
$ echo $HOME
/

Even though nobody has no true home, HOME is set to the root directory.

Yes. The POSIX specification requires the shell to set a valuefor $HOME:

HOME

The system shall initialize this variable at the time of login to be a pathname of the user's home directory. See <pwd.h>.

What about user nobody?

# su - nobody
No directory, logging in with HOME=/
$ echo $HOME
/

Even though nobody has no home, HOME is set to the root directory.

Yes. The POSIX specification requires the shell to set a value for $HOME:

HOME
The system shall initialize this variable at the time of login to be a pathname of the user's home directory. See pwd.h.

What about user nobody?

# su - nobody
No directory, logging in with HOME=/
$ echo $HOME
/

Even though nobody has no true home, HOME is set to the root directory.