XML::Twig is particularly well suited to do this transformation. Sorry, I don't have time to come up with the code right now.

Update: Contrary to claims made, that's not XML. 1 and 2 are not valid XML element names. If that isn't what you are actually using, the following code will do the trick:

use strict;
use warnings;

use XML::Twig;

my $t = XML::Twig->new(
   twig_handlers => {
      'p[@v!="YES"]' => sub { $_->delete },
   },
);

$t->parse(\*DATA);  # $t->parsefile( "file.xml");
$t->flush();

__DATA__
<?xml version="1.0" encoding="UTF-8" ?>
<e>
    <p id="1" v="YES">
        <c>The</c>
        <c>Bye</c>
    </p>
    <p id="2" v="NO">
        <c>Border</c>
        <c>Lamp</c>
    </p>
</e>
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