Update: Per the discussion here: https://groups.google.com/a/chromium.org/forum/#!topic/services-dev/Y9FKZf9n1ls, the approach to be taken in this case is to move the shutdown in question to happen on the IO thread, keyed off that thread's destruction via MessageLoopObserver. This will remove the direct dependency from browser_main_loop.cc to GamepadService.

Note that the approach we took in a similar case (https://codereview.chromium.org/2730333002) turns out to conflict with Lucky Luke's goal of removing MessageLoop::DestructionObserver (https://groups.google.com/a/chromium.org/forum/#!topic/services-dev/Y9FKZf9n1ls). However, we didn't come up with an alternative design while discussing this general problem (see that linked thread). Given this new information about Lucky Luke, the first question is: Can we eliminate GamepadService shutdown altogether?