I think that you should use a hash instead of an array to load file2, because a hash lookup is far more efficient than greping through a full array for each line of file1. Something like this (untested):

use strict;
use warnings;

my $second_file = "npn.txt";
open my $fh2, '<', $second_file or die "Cannot open  $second_file $!";
my %contents = map {chomp; $_ => 1} <$fh2>;
close $fh2;

my $first_file = "first_file.txt";
open my $fh1, '<', $first_file or die "Cannot open  $first_file $!";
while( my $line = <$fh1>) {
    chomp($line);
    my $field2 = (split /,/, $line)[1];
    print $line and next unless defined $field2;
    print $line unless defined $contents{$field2};
}
close $fh1;
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Please also take note of the way of opening files, considered to be more in line with commonly accepted best practices.