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

components/update_client/task_update.cc

Index: components/update_client/task_update.cc
diff --git a/components/update_client/task_update.cc b/components/update_client/task_update.cc
index d253466e7e1110d6ca3b266dca50f308dd0118d0..c6a72e6ee2f15444ede4eff5a2eaa30ff8694b0f 100644
--- a/components/update_client/task_update.cc
+++ b/components/update_client/task_update.cc
@@ -8,6 +8,7 @@
 #include "base/location.h"
 #include "base/single_thread_task_runner.h"
 #include "base/thread_task_runner_handle.h"
+#include "components/update_client/update_client.h"
 #include "components/update_client/update_engine.h"
 
 namespace update_client {
@@ -32,23 +33,30 @@
   DCHECK(thread_checker_.CalledOnValidThread());
 
   if (ids_.empty()) {
-    RunComplete(-1);
+    TaskComplete(Error::ERROR_UPDATE_INVALID_ARGUMENT);
     return;
   }
 
   update_engine_->Update(
       is_foreground_, ids_, crx_data_callback_,
-      base::Bind(&TaskUpdate::RunComplete, base::Unretained(this)));
+      base::Bind(&TaskUpdate::TaskComplete, base::Unretained(this)));
+}
+
+void TaskUpdate::Cancel() {
+  DCHECK(thread_checker_.CalledOnValidThread());
+
+  TaskComplete(Error::ERROR_UPDATE_CANCELED);
 }
 
 std::vector<std::string> TaskUpdate::GetIds() const {
   return ids_;
 }
 
-void TaskUpdate::RunComplete(int error) {
+void TaskUpdate::TaskComplete(int error) {
   DCHECK(thread_checker_.CalledOnValidThread());
 
-  callback_.Run(this, error);
+  base::ThreadTaskRunnerHandle::Get()->PostTask(
+      FROM_HERE, base::Bind(callback_, this, error));
 }
 
 }  // namespace update_client