On every page load, WordPress executes these functions in their respective order:

init();
parse_request($query_args);
send_headers();
query_posts();
handle_404();
register_globals();

where the main query is finished after query_posts(). Note that in this point in time, WordPress knows the template AND all the query variables like max_num_pages.

In handle_404(), if the main query has any posts in it, the function returns and continues to load the template. Else it sends a 404 HTTP status, aborts loading the template and loads the 404 template instead.

Since WordPress 4.5, there is a filter hook called pre_handle_404. If it's set to true, handle_404() returns (whether or not the main query has any posts!) and the template continues to load.

So after a lot of fiddling around, this finally works. Add this to your functions.php:

function rerun_query_when_404($bool = false, $query) {
  $paged = (get_query_var('paged')) ? intval(get_query_var('paged')) : 1;
  if (is_author() && ($paged > $query->max_num_pages))
    $bool = true;
  return $bool;
}
add_filter( 'pre_handle_404', 'rerun_query_when_404', 10, 2);

That's it. No editing of existing functions, clean and exactly what I wanted. Just make sure to update WordPress to version 4.5 (and above)!

On every page load, WordPress executes these functions in their respective order:

init();
parse_request($query_args);
send_headers();
query_posts();
handle_404();
register_globals();

where the main query is finished after query_posts(). Note that in this point in time, WordPress knows the template AND all the query variables like max_num_pages.

In handle_404(), if the main query has any posts, the function returns and WordPress continues to load the template. Else it sends a 404 HTTP status and loads the 404 template instead.

Since WordPress 4.5, there is a filter hook called pre_handle_404. If it's set to true, handle_404() returns (whether or not the main query has any posts!) and the template continues to load.

So after a lot of fiddling around, this finally works. Add this to your functions.php:

function ignore_404_past_max_page($bool = false, $query) {
  $paged = (get_query_var('paged')) ? intval(get_query_var('paged')) : 1;
  if (is_author() && ($paged > $query->max_num_pages))
    $bool = true;
  return $bool;
}
add_filter( 'pre_handle_404', 'ignore_404_past_max_page', 10, 2);

That's it! No editing of existing functions, clean and does exactly what you'd want it to do: prevent WP from 404ing. Just make sure to update WordPress to version 4.5 (and above)!

An unwanted side effect may be that now you can paginate untill PHP_INT_MAX and get empty pages (unless you add some get_the_author_meta() and get_wp_user_avatar() for example). You could probably memorize the maximum page number for each author in the database, then query it and compare it to $paged to set $bool to false in the function above. But I'm really happy with how it works now.

On every page load, WordPress executes these functions in their respective order:

init();
parse_request($query_args);
send_headers();
query_posts();
handle_404();
register_globals();

where the main query is finished after query_posts(). Note that in this point in time, WordPress knows the template AND all the query variables like max_num_pages.

In handle_404(), if the main query has any posts in it, the function returns and continues to load the template. Else it sends a 404 HTTP status, aborts loading the template and loads the 404 template instead.

Since WordPress 4.5, there is a filter hook called pre_handle_404. If it's set to true, handle_404() returns (whether or not the main query has any posts!) and the template continues to load.

So after a lot of fiddling around, this finally works. Add this to your functions.php:

function rerun_query_when_404($bool = false, $query) {
  $paged = (get_query_var('paged')) ? intval(get_query_var('paged')) : 1;
  if (is_author() && ($paged > $query->max_num_pages))
    $bool = true;
  return $bool;
}
add_filter( 'pre_handle_404', 'rerun_query_when_404', 10, 2);

That's it. No editing of existing functions, clean and exactly what I wanted.

On every page load, WordPress executes these functions in their respective order:

init();
parse_request($query_args);
send_headers();
query_posts();
handle_404();
register_globals();

where the main query is finished after query_posts(). Note that in this point in time, WordPress knows the template AND all the query variables like max_num_pages.

In handle_404(), if the main query has any posts in it, the function returns and continues to load the template. Else it sends a 404 HTTP status, aborts loading the template and loads the 404 template instead.

Since WordPress 4.5, there is a filter hook called pre_handle_404. If it's set to true, handle_404() returns (whether or not the main query has any posts!) and the template continues to load.

So after a lot of fiddling around, this finally works. Add this to your functions.php:

function rerun_query_when_404($bool = false, $query) {
  $paged = (get_query_var('paged')) ? intval(get_query_var('paged')) : 1;
  if (is_author() && ($paged > $query->max_num_pages))
    $bool = true;
  return $bool;
}
add_filter( 'pre_handle_404', 'rerun_query_when_404', 10, 2);

That's it. No editing of existing functions, clean and exactly what I wanted. Just make sure to update WordPress to version 4.5 (and above)!

I completely ditched the template_redirect stuff for this solution which FINALLY works. It hasn't much to do with handling 404s, I rather altered the query in the pre_get_posts hook:

function my_post_queries( $query ) {
  if (!is_admin() && $query->is_main_query()){
    if (is_author()){
      $query->set('posts_per_page', 3);
      // NEW CODE:
      $paged = (get_query_var('paged')) ? intval(get_query_var('paged')) : 1;
      global $original_page_request; // saves the original value of $paged because I'm about to alter it!
      if ($paged > $query->max_num_pages) {
        $query->set('paged', $query->max_num_pages); 
        // THE SETTING IN THE LINE ABOVE MUST BE SET TO max_num_pages!
        // (see NOTE below)
        $original_page_request = $paged;
    } else {
      $query->set('posts_per_page', 9);
    }
 }
}
add_action( 'pre_get_posts', 'my_post_queries' );

IMPORTANT NOTE

I came across something interesting, which is that paged MUST!! be set to $query->max_num_pages. If you set it to 1, max_num_pages is 0, even if you echo $query->max_num_pages in a line before. It completely breaks the solution here, pagination will always redirect to page 1.

From now on, get_query_var('paged') will always return the max_num_pages of my main query even if it says blabla/page/2 in the URL. So I'll use the global $original_page_request for everything that needs it.

In my author.php, the code

1. checks if max_num_pages is exceeded (= $original_page_request exists)

2. shows none of my main loop's posts after the page exceeds my main query's max_num_page

3. and then initializes my $secondloop

all in here:

// 1.
global $original_page_request;
if (isset($original_page_request)) {
    $is_within_max = false;
    $paged = $original_page_request;
} else {
    $is_within_max = true;
    $paged = get_query_var('paged') ? intval(get_query_var('paged')) : 1;
}

// 2.
if ($is_within_max && have_posts()) { ?>
    <div class="row archive-grid">
        <?php while (have_posts()) : the_post();
            include(locate_template('parts/loop-archive-grid.php'));
        endwhile; ?>
    </div>
<?php }
 
// 3.
$loop = new WP_Query(array(
    "post_type"      => "musikalbum",
    "posts_per_page" => 3,
    "author_name"    => get_query_var('author_name'),
    "paged"          => $paged
));

And in author_page_navi($loop) I've set the $paged variable similiarly:

if (isset($original_page_request))
  $paged = $original_page_request;
else
  $paged = intval(get_query_var("paged"));

Which works like a charm! A big thank you to the commenters though which helped me find the solution.

On every page load, WordPress executes these functions in their respective order:

init();
parse_request($query_args);
send_headers();
query_posts();
handle_404();
register_globals();

where the main query is finished after query_posts(). Note that in this point in time, WordPress knows the template AND all the query variables like max_num_pages.

In handle_404(), if the main query has any posts in it, the function returns and continues to load the template. Else it sends a 404 HTTP status, aborts loading the template and loads the 404 template instead.

Since WordPress 4.5, there is a filter hook called pre_handle_404. If it's set to true, handle_404() returns (whether or not the main query has any posts!) and the template continues to load.

So after a lot of fiddling around, this finally works. Add this to your functions.php:

function rerun_query_when_404($bool = false, $query) {
  $paged = (get_query_var('paged')) ? intval(get_query_var('paged')) : 1;
  if (is_author() && ($paged > $query->max_num_pages))
    $bool = true;
  return $bool;
}
add_filter( 'pre_handle_404', 'rerun_query_when_404', 10, 2);

That's it. No editing of existing functions, clean and exactly what I wanted.