Once I swap my $var = `unix_tool file_name`; to my $var = `cat script.pl`;, I get the expected output. What is unix_tool?

You should be able to split this into two steps (reading in from the backticks followed by the angle-bracket read). What happens when you copy the tool output into a DATA block and use that for your read, i.e.:

#!/usr/bin/perl
use strict;
use warnings;

$/ = "";
#This is just for example
while (<DATA>){
    print "------------------------------------------\n";
    print "$_";
    print "\n";
}
__DATA__
This is the output

From the tool.
[download]

Assuming this fails, post the modified snippet (scrubbed if necessary) and we can work from there.