It's clear that the example data you gave us doesn't give any matches, but if I modify it a bit I do get a match.

Code:

use strict;
use warnings;
use autodie;


open my $pids, '<', 'pids';
my %ids;
while (my $line = <$pids>) {
    chomp $line;
    my (undef, $id) = split /\|/, $line;
    $ids{$id} = 1;
}
close $pids;

open my $fids, '<', 'fids';
while (my $line = <$fids>) {
    my ($id, $rest) = split /;/, $line, 2;
    if ($ids{$id}) {
        print "Found id '$id' in line $line";
    }
}
close $fids;
[download]

FIDS:

810000001;08/17/1957
810000002;12/02/1975
810000003;12/22/1982
810000004;11/01/1967
810086196;02/07/1981
810000006;12/27/1967
810000007;05/09/1981
810000008;05/14/1976
810000009;10/24/1981
810000010;11/17/1943
[download]

pids (unchanged):

dn: cn=*****,ou=users,|810221480
dn: cn=*****,ou=users,|810039655
dn: cn=*****,ou=users,|810086196
dn: cn=*****,ou=users,|810008482
dn: cn=*****,ou=users,|810224329
[download]