The answer to your first requirement is to have (at it's most basic):
try
{
// Main application
}
catch // Though you might not want this
{
}
finally
{
// This code always executed even if application crashes.
}
However there are other considerations when dealing with Windows applications as RichardOD indicates in his comments here - http://msdn.microsoft.com/en-us/library/system.appdomain.unhandledexception.aspx and here http://msdn.microsoft.com/en-us/library/system.windows.forms.application.threadexception.aspx
The answer to your second requirement is no you can't trap the application being stopped in the debugger (or at least there's not a way I've come across). It just kills the process.
For instance if you have stopped at a break point and then press stop the code doesn't carry on executing to termination - it just exits.
UPDATE
I've just come across this question http://stackoverflow.com/questions/1033441/visual-studio-executing-clean-up-code-when-debugging-stops which has an answer that states:
You can use the DTE (VisualStudio
Automation Model) to write a macro
that will be invoked when a stop debug
happens, below is a snippet of the
idea.
Private Sub DebuggerEvents_OnEnterDesignMode(ByVal Reason As EnvDTE.dbgEventReason, ByRef ExecutionAction As EnvDTE.dbgExecutionAction) Handles DebuggerEvents.OnEnterDesignMode
If (Reason = dbgEventReason.dbgEventReasonStopDebugging) Then
// DO YOUR CLEAN UP CODE HERE
End If
End Sub
So while you can't trap the stopping of the execution in your application you can do something about it in Visual Studio.
NOTE: Answer provided by Shay Erlichmen not me!