Yes, I am a newcomer here, while being a regular StackO citizen. Also PerlMonks seemed very calm this morning...

I am getting some results from StackO and will post here any helpful result.

The best programs are the ones written when the programmer is supposed to be working on something else. - Melinda Varian

Quick question: what is the desired output?

With <thing_list> or without?

While dispatching the <thing> elements between the two files, I would expect each one being well formed, i.e. having both opening and closing tags for <thing_list> with perhaps no child elements inside.

Pretty much what Ikegami said on SO. You can see the order that the twigs and residual tags are being processed by modfying the code as follows:

use XML::Twig;
use IO::Tee;
use feature 'say';

open my $frufile, '>', 'fruit.xml' or die "fruit $!";
open my $vegfile, '>', 'veg.xml' or die "veg $!";

my $tee = IO::Tee->new($frufile, $vegfile);
select $tee;

my $twig=XML::Twig->new(
    twig_handlers => {
        thing  => \&magic,
        _default_  => sub { 
            print '_default_ for '.$_->name." [[[";
            $_[0]->flush($tee); #default filehandle = tee
            say "]]]";
            1; 
        },
    },
    pretty_print => 'none',
    empty_tags   => 'normal',
);

$twig->parse( *DATA );

sub magic {
    my ($thing, $element) = @_;
    print "magic for ". $element->{att}{type}." [[[";
    for ($element->{att}{type}) {
            if (/fruit/) {
                $thing->flush($frufile);
            } elsif (/vegetable/) {
                $thing->flush($vegfile);
            } else {
                $thing->purge;
            }
    }
    
    say "]]]";
    1;
}

__DATA__
<batch>
  <header>
    <foo>1</foo>
    <bar>2</bar>
    <baz>3</baz>
  </header>
  <thing_list>
  <thing type="fruit"     >Im an apple!</thing>
  <thing type="city"      >Toronto</thing>
  <thing type="vegetable" >Im a carrot!</thing>
  <thing type="city"      >Melrose</thing>
  <thing type="vegetable" >Im a potato!</thing>
  <thing type="fruit"     >Im a pear!</thing>
  <thing type="vegetable" >Im a pickle!</thing>
  <thing type="city"      >Patna</thing>
  <thing type="fruit"     >Im a banana!</thing>
  <thing type="vegetable" >Im an eggplant!</thing>
  <thing type="city"      >Taumatawhakatangihangakoauauotamateaturipuk
+akapikimaungahoronukupokaiwhenuakitanatahu</thing>
  </thing_list>
  <trailer>
    <chrzaszcz>A</chrzaszcz>
    <zdzblo>B</zdzblo>
  </trailer>
</batch>
[download]

Fruit.xml:

_default_ for foo[[[<batch><header><foo>1</foo>]]]
_default_ for bar[[[<bar>2</bar>]]]
_default_ for baz[[[<baz>3</baz>]]]
_default_ for header[[[</header>]]]
magic for fruit [[[<thing_list><thing type="fruit">Im an apple!</thing
+>]]]
magic for city [[[]]]
magic for vegetable [[[]]]
magic for city [[[]]]
magic for vegetable [[[]]]
magic for fruit [[[<thing type="fruit">Im a pear!</thing>]]]
magic for vegetable [[[]]]
magic for city [[[]]]
magic for fruit [[[<thing type="fruit">Im a banana!</thing>]]]
magic for vegetable [[[]]]
magic for city [[[]]]
_default_ for thing_list[[[</thing_list>]]]
_default_ for chrzaszcz[[[<trailer><chrzaszcz>A</chrzaszcz>]]]
_default_ for zdzblo[[[<zdzblo>B</zdzblo>]]]
_default_ for trailer[[[</trailer>]]]
_default_ for batch[[[</batch>]]]
[download]

Veg.xml

_default_ for foo[[[<batch><header><foo>1</foo>]]]
_default_ for bar[[[<bar>2</bar>]]]
_default_ for baz[[[<baz>3</baz>]]]
_default_ for header[[[</header>]]]
magic for fruit [[[]]]
magic for city [[[]]]
magic for vegetable [[[<thing type="vegetable">Im a carrot!</thing>]]]
magic for city [[[]]]
magic for vegetable [[[<thing type="vegetable">Im a potato!</thing>]]]
magic for fruit [[[]]]
magic for vegetable [[[<thing type="vegetable">Im a pickle!</thing>]]]
magic for city [[[]]]
magic for fruit [[[]]]
magic for vegetable [[[<thing type="vegetable">Im an eggplant!</thing>
+]]]
magic for city [[[]]]
_default_ for thing_list[[[</thing_list>]]]
_default_ for chrzaszcz[[[<trailer><chrzaszcz>A</chrzaszcz>]]]
_default_ for zdzblo[[[<zdzblo>B</zdzblo>]]]
_default_ for trailer[[[</trailer>]]]
_default_ for batch[[[</batch>]]]
[download]

Notice how the "<thing>" handler gets called after the tag is closed and flushes any other previous, unprocessed tag information before it.

I don't use stackoverflow much and couldn't comment there, which might have been more appropriate, but I took Ikegami's solution to your stackoverflow post and modified it just a little as below and the result seemed to do what you wanted with one pass.

my $tee = IO::Tee->new($frufile, $vegfile);

my $twig = XML::Twig->new(
... etc.
    twig_print_outside_roots => $tee,
...
);
$twig->parse( *DATA );
[download]

yes the answer of Ikegami (using the twig_roots instead of the twig_handlers) produce a result as asked, in a single pass.

But it is not the solution that I will use because of some additional needs :p : in the 'common' part of the produced files, an identifier need to be different in each file, thus when parsing that identifier with XML::Twig, I cannot presume of the value to put in, because I do not know the number of final files.

It results in a complicated program where I need to keep the beginning of the file in memory to let it be updated differently each time I write a chunk of <thing> in a separate file, while not keeping all the <thing>'s in memory because of the quantity of data... I am tweaking an XML::SAX::Writer based solution instead.