'This all works fine until I try to close the application when, predictably, WaitForSingleObject continues to wait and does not allow the app to close properly.'
Any app can close, no matter what its threads are doing. If you call ExitProcess(0) from any thread in your app, the app will close, no matter if there are threads waiting INFINITE on some API/sychro, sleeping, running on another processor, whatever. The OS will change the state of all theads that are not running to 'never run again' and use its interprocessor driver to hard-interrupt any other processors that are actually running your thread code. Once all the threads are stopped, the OS frees handles, segments etc and your app no longer exists.
Problems arise when developers try to 'cleanly' shut down threads that are stuck - like yours, when the app is closing. So..
Do you have a TThread.WaitFor, or similar, in an OnClose/OnCloseQuery handler, FormDestroy or destructor? If you have, and have no vital reason to ensure that the thread is terminated, just comment it out!
This allows the main form to close and so your code will finally reach the ExitProcess() it has been trying to get at since you clicked on the red cross button
You could, of coure, just call ExitProcess() yourself, but this may leave you with resources leaked in other proceses - database connections, for example.
'216/217 errors on close if I don't stop the threads'. This often happens because developers have followed the er... 'unfortunate' Delphi thread examples and communicate with threads by directly exchanging data between secondary thread fields and main thread fields, (eg. TThread.synchronize). This just sucks and is hell-bent on causing problems, even in the app run, never mind at shutdown when a form has been destroyed and a thread is trying to write to it or a thread has been destroyed and a main-thread form is trying ot call methods on it. It is much safer to communicate asynchronously with threads by means of queueing/PostMessaging objects that outlive both of them, eg. objects created in the thread/form and freed in the form/thread, or by means of a (thread-safe), pool of objects created in an initialization section. Forms can then close/free safely while associated threads may continue to pointlessly fill up objects for handling until the main form closes, ExitProcess() is reached and the OS annihilates the threads.
'My Form handle is invalid because it has closed but my thread tries to post a message to it'. If the PostMessage excepts, exit your thread. A better way is similar to the approach above - only post messages to a window that outlives all forms. Create one in an initialization section with a trivial WndProc that only handles one const message number that all threads use for posting. You can use wParam to pass the TwinControl instance that the thread is trying to communicate with, (usually a form variable), while lParam passes the object being communicated. When it gets a message from a thread, WndProc calls 'Peform' on the TwinControl passed and the TwinControl will get the comms object in a message-handler. A simple global boolean, 'AppClosing', say, can stop the WndProc calling Peform() on TwinControls that are freeing themselves during shutdown. This approach also avoids problems arising when the OS recreates your form window with a different handle - the Delphi form handle is not used and Windows will not recreate/change the handle of the simple form created in initialization.
I have followed these approaches for decades and do not get any shutdown problems, even with apps with dozens of threads slinging objects around on queues.
Rgds,
Martin