Delete "shutdown without closing browsers" path

chrome/browser/browser_shutdown.h

Index: chrome/browser/browser_shutdown.h
diff --git a/chrome/browser/browser_shutdown.h b/chrome/browser/browser_shutdown.h
index 208bb1dabbc040da294c46f4d45092bc3161577b..f53de37963a6aadec5e8fa1ad66cbbc6ca985d07 100644
--- a/chrome/browser/browser_shutdown.h
+++ b/chrome/browser/browser_shutdown.h
@@ -66,15 +66,6 @@ void SetTryingToQuit(bool quitting);
 // General accessor.
 bool IsTryingToQuit();
 
-// This is true on X during an END_SESSION initiated by X IO Error, when we
-// can no longer depend on the X server to be running. As a result we don't
-// explicitly close the browser windows, which can lead to conditions which
-// would fail checks.
-bool ShuttingDownWithoutClosingBrowsers();
-
-// Sets the ShuttingDownWithoutClosingBrowsers flag.
-void SetShuttingDownWithoutClosingBrowsers(bool without_close);
-
 }  // namespace browser_shutdown
 
 #endif  // CHROME_BROWSER_BROWSER_SHUTDOWN_H__