diff --git a/lib/kino/terminator.ex b/lib/kino/terminator.ex
index e1ddaa8c..55fa0071 100644
--- a/lib/kino/terminator.ex
+++ b/lib/kino/terminator.ex
@@ -30,8 +30,16 @@ defmodule Kino.Terminator do
         end
 
       if pid do
+        terminator = cross_node_name()
+
         Kino.Bridge.reference_object(pid, parent)
-        Kino.Bridge.monitor_object(pid, cross_node_name(), {:terminate, pid}, ack?: true)
+
+        with {:request_error, :terminated} <-
+               Kino.Bridge.monitor_object(pid, terminator, {:terminate, pid}, ack?: true) do
+          # If the group leader terminated, it is not going to monitor
+          # the process as we expect, so we terminate it immediately
+          send(terminator, {:terminate, pid})
+        end
       end
 
       resp
@@ -75,6 +83,11 @@ defmodule Kino.Terminator do
     {:noreply, Map.delete(state, pid)}
   end
 
+  def handle_info({:terminate, pid}, state) do
+    DynamicSupervisor.terminate_child(Kino.DynamicSupervisor, pid)
+    {:noreply, Map.delete(state, pid)}
+  end
+
   @impl true
   def handle_info({:DOWN, _, _, pid, reason}, state) do
     {parent, state} = Map.pop(state, pid)