[headless] Call StopLocalDevToolsHttpHandler only when needed.

headless/lib/browser/headless_browser_main_parts.cc

Index: headless/lib/browser/headless_browser_main_parts.cc
diff --git a/headless/lib/browser/headless_browser_main_parts.cc b/headless/lib/browser/headless_browser_main_parts.cc
index 0c75e132bab7e4a7a5126b4a28d4d5419b7c24da..b219480b6f784a47c8bb00f5ca5e21af91da58f0 100644
--- a/headless/lib/browser/headless_browser_main_parts.cc
+++ b/headless/lib/browser/headless_browser_main_parts.cc
@@ -26,18 +26,24 @@ void PlatformExit() {
 }  // namespace
 
 HeadlessBrowserMainParts::HeadlessBrowserMainParts(HeadlessBrowserImpl* browser)
-    : browser_(browser) {}
+    : browser_(browser)
+    , devtools_http_handler_started_(false) {}
 
 HeadlessBrowserMainParts::~HeadlessBrowserMainParts() {}
 
 void HeadlessBrowserMainParts::PreMainMessageLoopRun() {
-  if (browser_->options()->devtools_endpoint.address().IsValid())
+  if (browser_->options()->devtools_endpoint.address().IsValid()) {
     StartLocalDevToolsHttpHandler(browser_->options());
+    devtools_http_handler_started_ = true;
+  }
   PlatformInitialize(browser_->options()->window_size);
 }
 
 void HeadlessBrowserMainParts::PostMainMessageLoopRun() {
-  StopLocalDevToolsHttpHandler();
+  if (devtools_http_handler_started_) {
+    StopLocalDevToolsHttpHandler();
+    devtools_http_handler_started_ = false;
+  }
   PlatformExit();
 }