Fix TaskScheduler initialization in remoting processes.

remoting/host/it2me/it2me_native_messaging_host_main.cc

 // Copyright 2013 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 #include "remoting/host/it2me/it2me_native_messaging_host_main.h"
 
 #include <utility>
 
 #include "base/at_exit.h"
 #include "base/command_line.h"
@@ skipping 182 matching lines @@
       new It2MeNativeMessagingHost(needs_elevation, /*policy_service=*/nullptr,
                                    std::move(context), std::move(factory)));
 
   host->Start(native_messaging_pipe.get());
 
   native_messaging_pipe->Start(std::move(host), std::move(channel));
 
   // Run the loop until channel is alive.
   run_loop.Run();
 
+  // Block until tasks blocking shutdown have completed their execution.
+  base::TaskScheduler::GetInstance()->Shutdown();
+
   return kSuccessExitCode;
 }
 
 }  // namespace remoting