There's not enough information to answer this. I'd debug this by printing $array_ref_partial inside the while loop. I'm also not sure why you're pushing an array reference containing an array reference onto @rows_partial, but without seeing your printing code, I can't be sure that's wrong.

while ($array_ref_partial = $sth2->fetchrow_arrayref) {
    warn join(' | ', @$array_ref_partial), "\n";
    push @rows_partial, $array_ref_partial;
    push @partial_famids, $array_ref_partial->[1];
}
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On the other hand, since DBI reuses the same reference each time for fetchrow_arrayref(), you might mean something like this:

push @rows_partial, [ @$array_ref_partial ];
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That fits more in line with your comment about copying the array.