Found the problem. The while loop may not have a value populated, and the do has to await new data. Testing that when the payload is empty it terminates with the exit, since last causes an error.

do {
    if ( $input_xml ) {
        $dom = XML::LibXML->load_xml( string => $input_xml );
        my $isEmpty = !$dom->documentElement->hasChildNodes();
        last if $isEmpty;
        say $fh $input_xml;
        $offset = $offset + $record_limit;
        say $offset;
    }
} while ($input_xml = Get_CMDB_CI());
close($fh) || warn "close failed: $!";
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