Delete "shutdown without closing browsers" path

chrome/browser/browser_shutdown.cc

Index: chrome/browser/browser_shutdown.cc
diff --git a/chrome/browser/browser_shutdown.cc b/chrome/browser/browser_shutdown.cc
index 7ebee0d277ff076f62cfa34352684187522f5fbb..756563caf44510ea891a93365c568d244b364e18 100644
--- a/chrome/browser/browser_shutdown.cc
+++ b/chrome/browser/browser_shutdown.cc
@@ -62,9 +62,6 @@ namespace {
 // Whether the browser is trying to quit (e.g., Quit chosen from menu).
 bool g_trying_to_quit = false;
 
-// Whether the browser should quit without closing browsers.
-bool g_shutting_down_without_closing_browsers = false;
-
 #if defined(OS_WIN)
 upgrade_util::RelaunchMode g_relaunch_mode =
     upgrade_util::RELAUNCH_MODE_DEFAULT;
@@ -346,12 +343,4 @@ bool IsTryingToQuit() {
   return g_trying_to_quit;
 }
 
-bool ShuttingDownWithoutClosingBrowsers() {
-  return g_shutting_down_without_closing_browsers;
-}
-
-void SetShuttingDownWithoutClosingBrowsers(bool without_close) {
-  g_shutting_down_without_closing_browsers = without_close;
-}
-
 }  // namespace browser_shutdown