internal class Program
    {
        private static BackgroundWorker _worker;

        private static void Main()
        {
            _worker = new BackgroundWorker();
            _worker.DoWork += DoWork;
            _worker.RunWorkerAsync();
            
            //Спим, иначе background thread помрет
            Thread.Sleep(1000);
        }

        private static void DoWork(object obj, EventArgs e)
        {
            try
            {
                Foo foo = FooImpl;
                foo("Bar");
            }
            catch (Exception ex)
            {
                Debug.WriteLine("Catched");
            }
        }

        private static List<byte> FooImpl(string s)
        {
//            try
//            {
                throw new ApplicationException();
//            }
//            catch (Exception ex)
//            {
//                throw;
//            }
            
        }

        private delegate List<byte> Foo(string s);
    }