Reland of Change the update_client task runner behavior to continue on shutdown.

components/component_updater/component_updater_service_unittest.cc

Index: components/component_updater/component_updater_service_unittest.cc
diff --git a/components/component_updater/component_updater_service_unittest.cc b/components/component_updater/component_updater_service_unittest.cc
index c44c63b7c1482c3efde1bb0c6d43c337b379c141..9d78eb89ceb7370cdaac438f95028bb4ef33102c 100644
--- a/components/component_updater/component_updater_service_unittest.cc
+++ b/components/component_updater/component_updater_service_unittest.cc
@@ -71,6 +71,7 @@
   MOCK_CONST_METHOD2(GetCrxUpdateState,
                      bool(const std::string& id, CrxUpdateItem* update_item));
   MOCK_CONST_METHOD1(IsUpdating, bool(const std::string& id));
+  MOCK_METHOD0(Stop, void());
 
  private:
   ~MockUpdateClient() override;
@@ -190,12 +191,14 @@
 TEST_F(ComponentUpdaterTest, AddObserver) {
   MockServiceObserver observer;
   EXPECT_CALL(update_client(), AddObserver(&observer)).Times(1);
+  EXPECT_CALL(update_client(), Stop()).Times(1);
   component_updater().AddObserver(&observer);
 }
 
 TEST_F(ComponentUpdaterTest, RemoveObserver) {
   MockServiceObserver observer;
   EXPECT_CALL(update_client(), RemoveObserver(&observer)).Times(1);
+  EXPECT_CALL(update_client(), Stop()).Times(1);
   component_updater().RemoveObserver(&observer);
 }
 
@@ -250,6 +253,7 @@
       .WillRepeatedly(Invoke(&loop_handler, &LoopHandler::OnUpdate));
 
   EXPECT_CALL(update_client(), IsUpdating(id1)).Times(1);
+  EXPECT_CALL(update_client(), Stop()).Times(1);
 
   EXPECT_TRUE(component_updater().RegisterComponent(crx_component1));
   EXPECT_TRUE(component_updater().RegisterComponent(crx_component2));
@@ -301,6 +305,7 @@
   EXPECT_CALL(update_client(),
               Install("jebgalgnebhfojomionfpkfelancnnkf", _, _))
       .WillOnce(Invoke(&loop_handler, &LoopHandler::OnInstall));
+  EXPECT_CALL(update_client(), Stop()).Times(1);
 
   EXPECT_TRUE(cus.RegisterComponent(crx_component));
   EXPECT_TRUE(OnDemandTester::OnDemand(&cus, id));
@@ -345,6 +350,7 @@
   EXPECT_CALL(update_client(),
               Install("jebgalgnebhfojomionfpkfelancnnkf", _, _))
       .WillOnce(Invoke(&loop_handler, &LoopHandler::OnInstall));
+  EXPECT_CALL(update_client(), Stop()).Times(1);
 
   EXPECT_TRUE(component_updater().RegisterComponent(crx_component));
   component_updater().MaybeThrottle(