diff --git a/lib/broadway_cloud_pub_sub/options.ex b/lib/broadway_cloud_pub_sub/options.ex
index 0289879..d2681ec 100644
--- a/lib/broadway_cloud_pub_sub/options.ex
+++ b/lib/broadway_cloud_pub_sub/options.ex
@@ -74,6 +74,16 @@ defmodule BroadwayCloudPubSub.Options do
       """,
       default: :ack
     ],
+    on_draining: [
+      type:
+        {:custom, __MODULE__, :type_atom_action_or_nack_with_bounded_integer,
+         [[{:name, :on_success}, {:min, 0}, {:max, 600}]]},
+      doc: """
+      Configures the acking behaviour for the non consumed messages when draining.
+      See the "Acknowledgements" section below for all the possible values.
+      """,
+      default: {:nack, 0}
+    ],
     receive_interval: [
       type: :integer,
       default: @default_receive_interval,
diff --git a/lib/broadway_cloud_pub_sub/producer.ex b/lib/broadway_cloud_pub_sub/producer.ex
index 7050c90..1177461 100644
--- a/lib/broadway_cloud_pub_sub/producer.ex
+++ b/lib/broadway_cloud_pub_sub/producer.ex
@@ -138,6 +138,7 @@ defmodule BroadwayCloudPubSub.Producer do
   def init(opts) do
     receive_interval = opts[:receive_interval]
     client = opts[:client]
+    on_draining = opts[:on_draining]
 
     {:ok, config} = client.init(opts)
     ack_ref = opts[:broadway][:name]
@@ -146,6 +147,7 @@ defmodule BroadwayCloudPubSub.Producer do
      %{
        demand: 0,
        draining: false,
+       on_draining: on_draining,
        receive_timer: nil,
        receive_interval: receive_interval,
        client: {client, config},
@@ -205,6 +207,18 @@ defmodule BroadwayCloudPubSub.Producer do
     handle_receive_messages(%{state | receive_timer: nil})
   end
 
+  def handle_info(
+        {ref, messages},
+        %{draining: true, on_draining: on_draining, worker_task: %{ref: ref}} = state
+      ) do
+    # Drain messages, not acknowledging them and setting the ack to draining_deadline
+    messages
+    |> Enum.map(&Broadway.Message.configure_ack(&1, on_success: on_draining))
+    |> Broadway.Message.ack_immediately()
+
+    {:noreply, [], %{state | worker_task: nil}}
+  end
+
   def handle_info({ref, messages}, %{demand: demand, worker_task: %{ref: ref}} = state) do
     new_demand = demand - length(messages)
 
@@ -231,11 +245,7 @@ defmodule BroadwayCloudPubSub.Producer do
 
   @impl Producer
   def prepare_for_draining(state) do
-    if state.worker_task do
-      Task.shutdown(state.worker_task, :brutal_kill)
-    end
-
-    {:noreply, [], %{state | worker_task: nil, draining: true}}
+    {:noreply, [], %{state | draining: true}}
   end
 
   defp handle_receive_messages(%{draining: true} = state) do