Creates an observable that, when subscribed to, will subscribe to the underlying observable, but will not dispose that subscription when its own subscription is disposed.

gistfile1.cs

using System;
using System.Reactive;
using System.Reactive.Linq;

namespace RxFireAndForget
{
    public static class RxExtensions
    {
        /// <summary>
        /// Creates an observable that, when subscribed to, will subscribe to the underlying observable, 
        /// but will not dispose that subscription when its own subscription is disposed.
        /// </summary>
        public static IObservable<T> FireAndForget<T>(this IObservable<T> source)
        {
            return Observable
                .Create(
                    (IObserver<T> outerObserver) =>
                    {
                        var alive = true;

                        var innerObserver = Observer
                            .Create<T>(
                                n =>
                                {
                                    if (alive)
                                        outerObserver.OnNext(n);
                                },
                                e =>
                                {
                                    if (alive)
                                        outerObserver.OnError(e);
                                },
                                () =>
                                {
                                    if (alive)
                                        outerObserver.OnCompleted();
                                });
                        
                        // FIRE!
                        var disposable = source
                            .Subscribe(innerObserver);

                        return () =>
                        {
                            // STOP PROPAGATING EVENTS
                            alive = false;

                            // BUT FORGET TO DISPOSE
                        };
                    });
        }
    }


    class Program
    {


        static void Main(string[] args)
        {

        }
    }
}