Following/Followers Users list Using Ajax Pagination inside Author Profile

The problem is this line:

$curauth = (isset($_GET['author_name'])) ? get_user_by('slug', $author_name) : get_userdata(intval($author)); 

First you make the ajax call with an POST-request, that is the reason why the GET array is empty. Second the variable $author is not defined. So every time you call the script, the variable $curauth is empty.

A solution could be that you send the author name with the ajax call like the page or the nonce.

EDIT:
In the file author.php you detect the author data ($curauth) with the name (get_user_by('slug', $author_name)) or with the author id (get_userdata(intval($author))). To do the same on the server (function.php) you have to the send the same data via the ajax call.

<?php
// The variables tmp_author_name and tmp_author serve only as temporary storage.
// They controls how the data should be determined on the server.
$tmp_author_name="";
$tmp_author = 0;
if( isset($_GET['author_name']) )
{
    $tmp_author_name = $author_name;
}
else
{
    $tmp_author = intval($author);  
}
?>

<script type="text/javascript">

var ajaxurl = "<?php echo admin_url( 'admin-ajax.php' ); ?>";
var page = 2;
var canBeLoaded = true,
bottomOffset = 2000;

jQuery(function($) 
{

    $(window).scroll(function() 
    {

        if( $(document).scrollTop() > ( $(document).height() - bottomOffset ) && canBeLoaded == true ) 
        {

            canBeLoaded = false;
            /// add tmp_author_name and tmp_author to the ajax data array 
            var data = 
            {
                'action': 'user_following_by_ajax',
                'page': page,
                'security': '<?php echo wp_create_nonce("user_more_following"); ?>'
                'author_name': <?php echo esc_html($tmp_author_name); ?>,
                'author': <?php echo esc_html($tmp_author); ?>,

            };

            $.post(ajaxurl, data, function(response) 
            {
                $('#following').append(response);
                canBeLoaded = true;
                page++;
            });
        }
    });
});
</script>

On the server you read the post data and then detect the author.

add_action('wp_ajax_user_following_by_ajax', 'user_following_by_ajax_callback');
add_action('wp_ajax_nopriv_user_following_by_ajax', 'user_following_by_ajax_callback');

function user_following_by_ajax_callback() 
{
    check_ajax_referer('user_more_following', 'security');
    $paged = $_POST['page'];

    /// detect the author data with the name or with the author id
    $curauth = NULL;

    if( isset($_POST['author_name']) AND trim($_POST['author_name']) != '' )
    {
        $curauth = get_user_by('slug', trim($_POST['author_name']) );
    }
    elseif( isset($_POST['author']) AND intval($_POST['author']) > 0 )
    {
        $curauth = get_userdata( intval($_POST['author']) );    
    }

    if( !is_null($curauth) )
    {
        $include = get_user_meta($curauth->ID, '_pwuf_following', true);


        if ( !empty( $include ) ) 
        {

            echo 'Not followed anyone yet.';

        } 
        else 
        {
            //// continue with your existing code. /////
        }

    }
    else
    {
        echo 'Not followed anyone yet.';
    }
}