question

You will find the solution here.

Hi,@sunilmarulasiddaiah-7880. You could use the following code to prompt the application to close with an empty window.
Codebehind:

    private void Window_Loaded(object sender, RoutedEventArgs e)
         {
             this.Visibility = Visibility.Hidden;
             Window wnd = new Window();
             wnd.Width = 0;
             wnd.Height = 0;
             wnd.WindowStyle = WindowStyle.None;
    
             wnd.Loaded += delegate
             {
                 HwndSource source = (HwndSource)PresentationSource.FromDependencyObject(wnd);
               //  wnd.Visibility = Visibility.Hidden;
                 source.AddHook(WindowProc);
    
             };
    
             wnd.Show();
         }


    private static IntPtr WindowProc(IntPtr hwnd, int msg, IntPtr wParam, IntPtr lParam, ref bool handled)
         {
    
             switch (msg)
    
             {
    
                 case 0x11:
    
                 case 0x16:
                     MessageBox.Show("Close reason: WindowsShutDown");
                     
                     break;
    
                 case 0x112:
    
                     if ((LOWORD((int)wParam) & 0xfff0) == 0xf060)
                     {
                         MessageBox.Show("Close reason: UserClosing");
                          
                     }
    
                     break;
    
             }
    
             return IntPtr.Zero;
    
         }

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I created a WPF App (.Net Framework 4.8) using the Window_Loaded event to hide the window as shown above. Following is the process window tree shown by Spy++. The MainWindow is not visible and Spy++ is set to log all window messages that MainWindow receives.

Then I used Task Manager to End Task on WPFApp1.exe. The application closed but no window messages were seen by Spy++. It seems to me that Task Manager used TerminateProcess instead of sending a WM_SYSCOMMAND (SC_CLOSE) or WM_CLOSE message to the hidden window.

For comparison, this is what Spy++ sees when MainWindow is not hidden and the process is closed by Task Manager -

Consider a different way to allow a user to end the hidden window application -- use a notification area icon to allow the user to close the application instead of Task Manager.