That would be a straight up bug, wouldn't it? But I'm not sure that's right. I think we may be missing something because first it does delete the closing /site tag, plus, this below should have worked then because I'm specifically parsing the children -

use strict;
use warnings;
use XML::Twig;

my $xml = q(
<sites>
<site siteid="ONE">
   <name>name1</name>
   <address>address1</address>
   <contact>contact1</contact>
</site>
<site siteid="TWO">
   <name>name2</name>
   <address>address2</address>
   <contact>contact2</contact>
</site>
</sites>
);

my %handlers = ( 'name[string() =~ /name2/]' => sub {
                           my ($twig, $cnt) = @_;
                           my $parent = $cnt->parent;
                           foreach ($parent->children) {
                               print "Deleting: " . $_->text . "\n";
                               $_->delete;
                           }
                           $parent->delete;
                       }
                );
my $twig= new XML::Twig( PrettyPrint   => 'indented', twig_handlers =>
+ \%handlers);

$twig->parse($xml);
print $twig->sprint;
[download]

Gave the following output -

Deleting: name2
<sites>
  <site siteid="ONE">
    <name>name1</name>
    <address>address1</address>
    <contact>contact1</contact>
  </site>
  <address>address2</address>
  <contact>contact2</contact>
</sites>
[download]