Eliminate potential for flaky crash in BCKSFactory::SetTestingFactory().

components/browser_context_keyed_service/browser_context_keyed_service_factory.cc

Index: components/browser_context_keyed_service/browser_context_keyed_service_factory.cc
diff --git a/components/browser_context_keyed_service/browser_context_keyed_service_factory.cc b/components/browser_context_keyed_service/browser_context_keyed_service_factory.cc
index 8f2bc729f06b474421eb06b26e3e7322e8ff4e3d..04785bb436b045a5ae37204c737981e5b1ceb509 100644
--- a/components/browser_context_keyed_service/browser_context_keyed_service_factory.cc
+++ b/components/browser_context_keyed_service/browser_context_keyed_service_factory.cc
@@ -20,6 +20,12 @@ void BrowserContextKeyedServiceFactory::SetTestingFactory(
   // destruction.
   bool add_context = ArePreferencesSetOn(context);
 
+  // Ensure that |context| is not marked as stale (e.g., due to it aliasing an
+  // instance that was destroyed in an earlier test) in order to avoid accesses
+  // to |context| in |BrowserContextShutdown| from causing
+  // |AssertBrowserContextWasntDestroyed| to raise an error.
+  dependency_manager_->MarkBrowserContextLiveForTesting(context);
+
   // We have to go through the shutdown and destroy mechanisms because there
   // are unit tests that create a service on a context and then change the
   // testing service mid-test.