naive way

app/controllers/server/websites_controller.rb

@@ -27,6 +27,10 @@ class Server::WebsitesController < Server::ApplicationController
 
   def update
     @website.update(website_params)
+    @website.recursive_dependencies.each do |dependency|
+      next unless dependency.respond_to?(:university_id)
+      dependency.update_column :university_id, @website.university_id
+    end
     redirect_to server_website_path(@website), notice: t('admin.successfully_updated_html', model: @website.to_s)
   end
 

app/views/server/websites/edit.html.erb

@@ -3,7 +3,7 @@
   <%= f.error_notification %>
   <%= f.error_notification message: f.object.errors[:base].to_sentence if f.object.errors[:base].present? %>
 
-  <%= f.association :university %>
+  <%= f.association :university, include_blank: false %>
 
   <% content_for :action_bar_right do %>
     <%= submit f %>