Here is one way to do this with XML::LibXML.

#!/usr/bin/perl
use warnings;
use strict;
use XML::LibXML;

my $xmlfile = 'test.xml';

my $parser = XML::LibXML->new();
my $doc    = $parser->parse_file($xmlfile);

my ($li_node) = $doc->findnodes("//li");

my ($p_element) = $doc->findnodes("//li/p");

foreach ($p_element->childNodes) {
    $li_node->appendChild( $_ );
}
$li_node->removeChild( $p_element );
    
print $doc->toString;
[download]

Contents of test.xml:

<?xml version="1.0" encoding="utf-8"?>
<li>
  <p>
   Some <b>text<c1> here</c1></b>
  </p>
</li>
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Result:

<?xml version="1.0" encoding="utf-8"?>
<li>
  

   Some <b>text<c1> here</c1></b>
  </li>
[download]