This situation arises when you use ShellExecuteEx or CreateProcess to start another application from your GUI application, then try to wait synchronously using WaitForSingleObject on its process handle.
The problem arises because your application has a window but isn't pumping messages. If the spawned application invokes SendMessage with one of the broadcast targets (HWND_BROADCAST or HWND_TOPMOST), then the SendMessage won't return to the new application until all applications have handled the message - but your app can't handle the message because it isn't pumping messages.... so the new app locks up, so your wait never succeeds.... DEADLOCK.
If you have absolute control over the spawned application, then there are measures you can take, such as using SendMessageTimeout rather than SendMessage (e.g. for DDE initiations, if anybody is still using that). But there are situations which cause implicit SendMessage broadcasts over which you have no control, such as using the SetSysColors API for instance.
The only safe ways round this are (a) split off the Wait into a separate thread, (b) use a timeout on the Wait and use PeekMessage in your Wait loop to ensure that you pump messages, (c) use the MsgWaitForMultipleObjects API instead. C is probably the simplest option to implement.