BackgroundWorker RunWorkerCompleted Event
If the BackgroundWorker was created from the UI thread, then the RunWorkerCompleted event will also be raised on the UI thread.
If it was created from a background thread, the event will be raised on an undefined background thread (not necessarily the same thread, unless you're using a custom SynchronizationContext).
Interestingly, this doesn't seem to be all that well-documented on MSDN. The best reference I was able to find was here:
The preferred way to implement multithreading in your application is to use the BackgroundWorker component. The BackgroundWorker component uses an event-driven model for multithreading. The background thread runs your DoWork event handler, and the thread that creates your controls runs your ProgressChanged and RunWorkerCompleted event handlers. You can call your controls from your ProgressChanged and RunWorkerCompleted event handlers.
From my observation, the RunWorkerCompleted is executed on the thread that called RunWorkerAsync, which is not necessarily the thread that CREATED the background worker.