Maybe the OP doesn't want to really share data, but wants the Parent class to provide fallback data. But maybe that shouldn't be per-class but more per-instance. Anyway, I would also recommend the OP use a getter/setter approach instead of reaching into the objects:

sub get( $self, $item ) {
    if( exists $self->{data}->{ $item }) {
        return $self->{data}->{ $item }
    } elsif( $self->{parent_data}->{ $item }) {
        return $self->{parent_data}->{ $item }
    }
}

sub set( $self, $item, $value ) {
    return $self->{data}->{ $item } = $value;
}
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