post_title in save_post action

Without knowing the surrounding code, it is hard to tell what the problem might be,
but you said you checked the $post variable. Maybe the $post variable is not set properly, the save_post action only gives you the post id:

function get_post_title($post_id) {
  $post = get_post($post_id);

  if (empty($post->post_title)) {
    // No title set, put in your code
  }
}
add_action('save_post', 'get_post_title');