Fix TaskScheduler initialization in remoting processes.

remoting/host/remoting_me2me_host.cc

 // Copyright (c) 2012 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.
 //
 // This file implements a standalone host process for Me2Me.
 
 #include <stddef.h>
 
 #include <cstdint>
 #include <memory>
@@ skipping 1652 matching lines @@
   // TODO(wez): The HostProcess holds a reference to itself until Shutdown().
   // Remove this hack as part of the multi-process refactoring.
   int exit_code = kSuccessExitCode;
   ShutdownWatchdog shutdown_watchdog(
       base::TimeDelta::FromSeconds(kShutdownTimeoutSeconds));
   new HostProcess(std::move(context), &exit_code, &shutdown_watchdog);
 
   // Run the main (also UI) message loop until the host no longer needs it.
   base::RunLoop().Run();
 
+  // Block until tasks blocking shutdown have completed their execution.
+  base::TaskScheduler::GetInstance()->Shutdown();
+
   return exit_code;
 }
 
 }  // namespace remoting