I don't know how likely it is that HOME is undefined, but it seems to me that
Eiffel should do something reasonable if it isn't.  The only reasonable thing
to do on a Unix platform is to call `getpwuid' to find out what the home
directory is.  There is no other way to find out, as far as I know.  The
shell has to call getpwuid or getpwuid_r once at login to set the "home"
shell variable and the HOME environment variable values.

I don't think the C code to do this is very complicated.  There is a similar
example in file.c routine `file_owner'.

Another option would be to return "" (empty string) if HOME is undefined
but presumably this would violate the expectation of callers of 
{EXECUTION_ENVIRONMENT}.home_directory_name.  If you did this, then estudio
could refuse to run if HOME is not set, just as it does if ISE_EIFFEL is not
set.  I don't think this is a great solution.

A third option is to raise an exception if HOME environment variable is not
set, but then all programs would have to catch it to display a nice
error message.