Managing the lifetime of a process I don't control - winapi

Question

I'm using Chromium Embedded Framework 3 (via CEFGlue) to host a browser in a third-party process via a plugin. CEF spins up various external processes (e.g. the renderer process) and manages the lifetime of these.
When the third-party process exits cleanly, CefRuntime.Shutdown is called and all the processes exit cleanly. When the third-party process exits badly (for example it crashes) I'm left with CEF executables still running and this (sometimes) causes problems with the host application meaning it doesn't start again.
I'd like a way to ensure that whatever manner the host application exits CefRuntime.Shutdown is called and the user doesn't end up with spurious processes running.
I've been pointed in the direction of job objects (see here) but this seems like it might be difficult to ship in a real solution as on some versions of Windows it requires administrative rights.
I could also set CEF to run in single process mode, but the documentation specifies that this is really for "debugging" only, so I'm assuming shipping this in production code is bad for some reason (see here).
What other options do I have?
Following on from the comments, I've tried passing the PID of the host process through to the client (I can do this by overriding OnBeforeChildProcessLaunch). I've then created a simple watchdog with the following code:
ThreadPool.QueueUserWorkItem(_ => {
var process = Process.GetProcessById(pid);
while (!process.WaitForExit(5000)) {
Console.WriteLine("Waiting for external process to die...");
}
Process.GetCurrentProcess().Kill();
});
I can verify in the debugger that this code executes and that the PID I'm passing into it is correct. However, if I terminate the host process I find that the thread simply dies in a way that I can't control and that the lines following the while loop are never executed (even if I replace it with a Console.WriteLine I never see any more messages printed from this thread.

Answer 1

For posterity, the solution suggested by #IInspectable worked, but in order to make it work I had to switch the implementation of of the external process to use the non-multi threaded message loop.
settings.MultiThreadedMessageLoop = false;
CefRuntime.Initialize(mainArgs, settings, cefWebApp, IntPtr.Zero);
Application.Idle += (sender,e) => {
if (parentProcess.HasExited) Process.GetCurrentProcess().Kill();
CefRuntime.DoMessageLoopWork();
}
Application.Run();