The is a simple c# console app that demonstrates various behaviors when .NET Tasks do or do not have their exceptions observed.

Task Exception Policy Test.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading;
using System.Threading.Tasks;

namespace UnobservedExceptions
{
    // NOTES: 
    // 1) run this in a 4.5 app and watch the behavior differences when changing the
    // ThrowUnobservedTaskExceptions config option
    //    <configuration>
    //      <startup> 
    //        <supportedRuntime version = "v4.0" sku=".NETFramework,Version=v4.5.2" />
    //      </startup>
    //      <runtime>
    //        <ThrowUnobservedTaskExceptions enabled = "true" />
    //      </ runtime >
    //    </ configuration >
    //
    // 2) Run this in RELEASE mode not DEBUG mode 
    
    class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine("Options:");
            Console.WriteLine("1 - Don't observe, don't collect");
            Console.WriteLine("2 - Don't observe, do collect");
            Console.WriteLine("3 - do observe, don't collect");
            Console.WriteLine("4 - do observe, do collect");
            string cmd = Console.ReadLine();
            switch(cmd)
            {
                case "1":
                    RunTest(false, false);
                    break;
                case "2":
                    RunTest(false, true);
                    break;
                case "3":
                    RunTest(true, false);
                    break;
                case "4":
                    RunTest(true, true);
                    break;
            }
        }

        private static void RunTest(bool observe, bool collect)
        {
            Console.WriteLine($"Observe:{observe}, Collect:{collect}");

            Task t = Task.Run(() =>
            {
                Console.WriteLine("Throwing!");
                throw new NotImplementedException("Cant do that!");
            });

            Thread.Sleep(100);  // wait here to let the task get scheduled and run

            if (observe && t.Exception != null)
            {
                Console.WriteLine($"Found an exception! {t.Exception.Message}");
            }

            if (collect)
            {
                // force a garbage collection and the Task finalizers to run
                Console.WriteLine("Press enter to collect");
                Console.ReadLine();
                GC.Collect();
                GC.WaitForPendingFinalizers();
            }

            Console.WriteLine("Finished");
            Console.ReadLine();
        }
    }
}