XPath '//cat[not(@meow)]' will identify such nodes.

XML::LibXML example:

use strict;
use warnings;

use XML::LibXML qw( );

my $xml = <<'__EOI__';
<root>
<cat tail='text' meow='text'/>
<cat tail='text' meow=''/>
<cat tail='text'/>
<dog tail='text' bark='text'/>
</root>
__EOI__

my $doc  = XML::LibXML->new()->parse_string($xml);
my $root = $doc->documentElement();

for my $node ($root->findnodes('//cat[not(@meow)]')) {
   $node->setAttribute(meow => 'default');
}

print $doc->toString();
[download]

<?xml version="1.0"?>
<root>
<cat tail="text" meow="text"/>
<cat tail="text" meow=""/>
<cat tail="text" meow="default"/>
<dog tail="text" bark="text"/>
</root>
[download]

Or if you prefer, $node->parentNode()->removeChild($node); would remove the offending node.