As per our conversation in the CB,

use strict;
use warnings;

open(my $sav_fh, '<', 'saved_system.txt'  ) or die;
open(my $cur_fh, '<', 'current_system.txt') or die;

my @sav_files = sort <$sav_fh>;
my @cur_files = sort <$cur_fh>;

my @rem_files;
my @new_files;

while (@sav_files && @cur_files) {
    if ($sav_files[0] lt $cur_file[0]) {
        push @rem_files, shift(@sav_files);
    }
    elsif ($sav_files[0] gt $cur_file[0]) {
        push @new_files, shift(@cur_files);
    }
    else {
        shift @sav_files;
        shift @cur_files;
    }
}

push @rem_files, @sav_files;
push @new_files, @cur_files;

open(my $rem_fh, '>', 'removed.txt') or die;
print $rem_fh @rem_files;
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