Prevent tabs sync during browser shutdown.

components/sync_sessions/sessions_sync_manager.h

Index: components/sync_sessions/sessions_sync_manager.h
diff --git a/components/sync_sessions/sessions_sync_manager.h b/components/sync_sessions/sessions_sync_manager.h
index d685c65cd42b58f7cb22d4b2b3b6810761165eec..293a45c4994bc9b964a3f8801f9c0de27be7a138 100644
--- a/components/sync_sessions/sessions_sync_manager.h
+++ b/components/sync_sessions/sessions_sync_manager.h
@@ -101,6 +101,11 @@ class SessionsSyncManager : public syncer::SyncableService,
   void OnLocalTabModified(SyncedTabDelegate* modified_tab) override;
   void OnFaviconsChanged(const std::set<GURL>& page_urls,
                          const GURL& icon_url) override;
+  void SetAllBrowsersClosing(bool browsers_closing) override;
+
+  bool GetAllBrowsersClosingForTesting();
+  static void SetInitialAllBrowsersClosingValueForTesting(
+      bool initial_browsers_closing);
 
   // Returns the tag used to uniquely identify this machine's session in the
   // sync model.
@@ -286,6 +291,10 @@ class SessionsSyncManager : public syncer::SyncableService,
   // proves that we are still relevant.
   bool local_tab_pool_out_of_sync_;
 
+  // Indicates that browsers are closing, so we shouldn't sync tabs closing
+  // events.
+  bool all_browsers_closing_;
+
   syncer::SyncPrefs* sync_prefs_;
 
   std::unique_ptr<syncer::SyncErrorFactory> error_handler_;