https://crash.corp.google.com/browse?reportid=c19bf85880000000

BrowserProcessImpl::Pin()
KeepAliveRegistry::OnKeepAliveStateChanged(bool)
ScopedKeepAlive::ScopedKeepAlive(KeepAliveOrigin,KeepAliveRestartOption)
BackgroundModeManager::UpdateKeepAliveAndTrayIcon()
BackgroundModeManager::StartBackgroundMode()
BackgroundModeManager::OnClientsChanged([...])
BackgroundModeManager::RegisterTrigger(Profile *,BackgroundTrigger *,bool)
PushMessagingServiceImpl::IncreasePushSubscriptionCount(int,bool)
PushMessagingServiceImpl::DidSubscribeWithEncryptionInfo([...])
[...]
gcm::GCMEncryptionProvider::DidCreateEncryptionInfo([...])
[...]
gcm::GCMKeyStore::DidStoreKeys(gcm::KeyPair const &,std::basic_string<char,std::char_traits<char>,std::allocator<char> > const &,base::Callback<void ,1,1> const &,bool)
[...]
base::MessageLoop::RunTask(base::PendingTask *)
[...]
ChromeBrowserMainParts::MainMessageLoopRun(int *)


I suppose the BackgroundModeManager could skip the trigger registration if we are shutting down, but it might be better for the message to be entirely skipped in the first place.