Treat background finalization as another GC task so it won't run in parallel with the marker.

runtime/vm/service.cc

 // Copyright (c) 2013, the Dart project authors.  Please see the AUTHORS file
 // for details. All rights reserved. Use of this source code is governed by a
 // BSD-style license that can be found in the LICENSE file.
 
 #include "vm/service.h"
 
 #include "include/dart_api.h"
 #include "include/dart_native_api.h"
 #include "platform/globals.h"
 
@@ skipping 3530 matching lines @@
   }
 
   void Append(PersistentHandle* persistent_handle) {
     JSONObject obj(handles_);
     obj.AddProperty("type", "_PersistentHandle");
     const Object& object = Object::Handle(persistent_handle->raw());
     obj.AddProperty("object", object);
   }
 
   void Append(FinalizablePersistentHandle* weak_persistent_handle) {
+    if (!weak_persistent_handle->raw()->IsHeapObject()) {
+      return;  // Free handle.
+    }
+
     JSONObject obj(handles_);
     obj.AddProperty("type", "_WeakPersistentHandle");
     const Object& object =
         Object::Handle(weak_persistent_handle->raw());
     obj.AddProperty("object", object);
     obj.AddPropertyF(
         "peer",
         "0x%" Px "",
         reinterpret_cast<uintptr_t>(weak_persistent_handle->peer()));
     obj.AddPropertyF(
@@ skipping 614 matching lines @@
     if (strcmp(method_name, method.name) == 0) {
       return &method;
     }
   }
   return NULL;
 }
 
 #endif  // !PRODUCT
 
 }  // namespace dart