I think that you're looking for something like this:

#!/usr/bin/perl

use strict;
use warnings;
use diagnostics;

open(LOG, '>', '/root/Desktop/log.out') or die "Can't redirect stdout:
+ $!";
open(CMD, 'ls |');
open(STDERR, '>&', STDOUT) or die "Can't redirect stderr: $!";
open(STDERR, '>', 'LOG_FILE') or die "Can't redirect stderr: $!";
print "\nhere1\n";
while (<CMD>) {
    print_stuff ($_);
}

sub print_stuff {
      my ($line) = @_;
      print LOG $line;  
      print $line;
}
print "\nhere2\n";
close LOG;
close CMD;
close STDERR;

exit;
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