Před:

$file_edit = fopen('chat/lib/data/users.php', 'r+');
fseek($file_edit, -3,SEEK_END);
fwrite($file_edit, $new_user_information);
fclose($file_edit);

$handle = fopen('chat/lib/data/users.php', 'r');
while (($buffer = fgets($handle)) !== false) {
    if (strpos($buffer, $_POST['username']) !== false) {
       die('Jmeno jiz existuje, pouzij jine!');
    }      
}
fclose($handle);