I haven't read through the rewrite.

What I meant about passing a code reference is using an anonymous sub.

# create code reference
my $anon_sub = sub { print "Hello world!\n" };
# execute the code
$anon_sub->();
[download]

For Daemonize, it would look something like...

my $run = sub { die 'unfinished' };
my $d = Daemonize->new( run => $run );

# later, inside Daemonize
    $self->{run}->( $self );
[download]

I think it would be a good idea to pass the Daemonize object to the sub itself (as I did in the example) so it can call methods on it (like logging) if it wants to.

I'm not quite clear about what you're trying to do with $SIG{__DIE__}, but you might want an END block or a DESTROY method instead.