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

extensions/browser/updater/update_service_unittest.cc

Index: extensions/browser/updater/update_service_unittest.cc
diff --git a/extensions/browser/updater/update_service_unittest.cc b/extensions/browser/updater/update_service_unittest.cc
index f570303f382156c211bc2edefa307961040bba63..fe2aefe939444ef7c91a5742ac98de9313c42044 100644
--- a/extensions/browser/updater/update_service_unittest.cc
+++ b/extensions/browser/updater/update_service_unittest.cc
@@ -46,6 +46,7 @@
     return false;
   }
   bool IsUpdating(const std::string& id) const override { return false; }
+  void Stop() override {}
 
  protected:
   friend class base::RefCounted<FakeUpdateClient>;