// User IDs from the form.
$form_data = [
    14,
    2346,
    125,
];

// Clear previous data in case user unsubscribed someone.
delete_user_meta( $updated_user_id, 'subscribing_authors' );

// Add each subscribed author ID as a single entry.
foreach( $form_data as $author_id ) {
    add_user_meta( $updated_user_id, 'subscribing_authors', $author_id );
}