If no posts in category display Form instead of not found

In your category.php ( or custom taxonomy archive template ), you should add the form code in the else case of your check if there are posts

e.g.

if(have_posts()){
    // do the post loop
} else {
    // display a form that takes user details for future posts
}

If there is no category.php you can copy and rename your index.php, and you can do the same for individual categories, e.g. category-example.php will be sued instead of category.php for the example category