I don't think you can get ignore_elts to work the way you want. You could write a handler to delete the titles you want to skip:

my $sel = 'title';
my $twig = XML::Twig->new(
    pretty_print => 'indented',
    twig_roots  => { "$sel" => \&parse_title },
);

$twig->parsefile('1.xml');

$twig->print;

sub parse_title {
    my ($t,$title) = @_;
    $title->delete if $title->get_xpath( 'name/fnm[@letter="a"]' );
}
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Output using your example XML:

<?xml version="1.0"?>
<titles>
  <title id="1">testing<name><snm>Houston</snm>, <fnm letter="c">Carl<
+/fnm></name><g>69</g><ppg>20.1</ppg><rpg>3.4</rpg><apg>2.8</apg><blk>
+14</blk></title>
  <title id="3">testign
    <name>Houston
    <fnm j="b">Bob</fnm><g>49</g><title>
    testing the sub title in title
    </title><title>
    this is pcdata in subtitle
        <title>
        second sub level
        </title></title></name></title>
</titles>
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