A dup needs printed to the file each time it appears.

(Untested)

...
while (<IN>) {
    $seen{$_}++;
}

foreach my $id (sort keys %seen) {
    if ( $seen{$id} == 1 ) {
        print UNQ "$id\n";
    }
    else {
        print DUP "$id\n" foreach 1..$seen{$id};
    }
}
...
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