[Chromoting] Moving common logic responsible for launching child processes to WorkerProcessLauncher…

remoting/base/stoppable.cc

Index: remoting/base/stoppable.cc
diff --git a/remoting/base/stoppable.cc b/remoting/base/stoppable.cc
index 88b3c95ef953cdf9fbe840ab4db168954d745a40..046ac424ac3901612110c24a2e2a68b5bff17924 100644
--- a/remoting/base/stoppable.cc
+++ b/remoting/base/stoppable.cc
@@ -26,8 +26,10 @@ void Stoppable::Stop() {
 
   if (state_ == kRunning) {
     state_ = kStopping;
-    DoStop();
   }
+
+  // DoStop() can be called multiple times.
+  DoStop();
 }
 
 void Stoppable::CompleteStopping() {