Looks like a ferfect task for Text::CSV_XS's csv using a filter:

$ cat npn.txt
11111111
10001781
11111222
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$ cat first_file.txt
abc,,,,
abc,10001781,,,
abc,10001782,,,
abd,10001783,,,
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$ cat test.pl
use strict;
use warnings;
use Text::CSV_XS "csv";

my %npn = map { chomp; $_ => 1 } do { local @ARGV = "npn.txt"; <> };

csv (in => "first_file.txt", filter => { 2 => sub { !exists $npn{$_} }
+});
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$ perl test.pl
abc,,,,
abc,10001782,,,
abd,10001783,,,
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