Ajax search box displays nothing if taxonomy doesn’t exist

You can always check the response. I don’t know what your php function returns but I assume it returns nothing while not found. Lets modify the fetch() function to check whether response is empty or not. From the code bellow you will get the idea of where to implement the popup.

function fetch() {
    var keyword = jQuery('#listing_tags').val();
    var myDiv = document.getElementById("ajaxbox");
    if (keyword != "") {
        myDiv.style.display = "block";
    } else {
        myDiv.style.display = "none";
    }
    jQuery.post('<?php echo admin_url('
        admin - ajax.php '); ?>', {
            'action': 'my_action',
            'keyword': keyword
        },
        function(response) {
            jQuery('#datafetch').html('');
            if(response.trim()==''){
                //This code will run when response is empty
                jQuery('#datafetch').append('<p>no search results found</p>');
            }else{
                //This code will run if there is valid response
                jQuery('#datafetch').append(response);
            }
        });
}