Program.cs

using System;
using System.Diagnostics;
using System.Net;
using System.Net.Sockets;
using System.Threading.Tasks;

namespace SlowClose
{
    class Program
    {
        const int PORT = 8080;
        const long SERVER_SEND_CHUNK_SIZE = 4 * 1024;
        const long SERVER_SEND_CHUNK_COUNT = 8 * 1024;
        const long CLIENT_RECEIVE_CHUNK_SIZE = 64 * 1024;
        const double CLIENT_TARGET_BYTES_PER_SECOND = 2 * 1024 * 1024;

        static void Main(string[] args)
        {
            Console.WriteLine("Hello World!");
            Task.WaitAll(RunServer(), RunClient());
        }

        static async Task RunServer()
        {
            using (var listenSocket = new Socket(AddressFamily.InterNetwork, SocketType.Stream, ProtocolType.Tcp))
            {
                listenSocket.Bind(new IPEndPoint(IPAddress.Loopback, PORT));
                listenSocket.Listen(0);

                using (var socket = await listenSocket.AcceptAsync())
                {
                    var sendChunk = new byte[SERVER_SEND_CHUNK_SIZE].AsMemory();
                    var receiveChunk = new byte[1].AsMemory();

                    var readTask = socket.ReceiveAsync(receiveChunk, SocketFlags.None);

                    for (int i = 0; i < SERVER_SEND_CHUNK_COUNT; i++)
                    {
                        //Console.WriteLine("Seinding");
                        await socket.SendAsync(sendChunk, SocketFlags.None);
                        //Console.WriteLine("Sent!!!!!");
                    }

                    Console.WriteLine("Shuting down socket.");
                    socket.Shutdown(SocketShutdown.Both);
                    Console.WriteLine("Shut down socket.");

                    try
                    {
                        var bytesRead = await readTask;
                        Console.WriteLine("Server read task completed gracefully with {0} bytes read", bytesRead);
                    }
                    catch (Exception ex)
                    {
                        Console.WriteLine("Server read task completed with error: {0}", ex);
                    }
                }
            }

            Console.WriteLine("Server sockets disposed");
        }

        static async Task RunClient()
        {
            using (var socket = new Socket(AddressFamily.InterNetwork, SocketType.Stream, ProtocolType.Tcp))
            {
                var stopwatch = new Stopwatch();
                stopwatch.Start();

                var totalBytesReceived = 0;
                var receiveBuffer = new byte[CLIENT_RECEIVE_CHUNK_SIZE].AsMemory();

                await socket.ConnectAsync(new IPEndPoint(IPAddress.Loopback, 8080));

                while (totalBytesReceived < SERVER_SEND_CHUNK_SIZE * SERVER_SEND_CHUNK_COUNT)
                {
                    //Console.WriteLine("Receiving");
                    var received = await socket.ReceiveAsync(receiveBuffer, SocketFlags.None);
                    //Console.WriteLine("Received: {0}", received);

                    if (received == 0)
                    {
                        Console.WriteLine("Unexpectedly observed end of data");
                        return;
                    }

                    totalBytesReceived += received;

                    var expectedTimeElapsed = TimeSpan.FromSeconds(totalBytesReceived / CLIENT_TARGET_BYTES_PER_SECOND);
                    var timeElapsed = stopwatch.Elapsed;

                    if (timeElapsed + TimeSpan.FromSeconds(1) < expectedTimeElapsed)
                    {
                        Console.WriteLine("Delaying {0} seconds after receiving {1} bytes in {2} seconds", expectedTimeElapsed - timeElapsed, totalBytesReceived, timeElapsed);
                        await Task.Delay(expectedTimeElapsed - timeElapsed);
                    }
                }
            }

            Console.WriteLine("Read all data");
        }
    }
}

Sample output (no repro 😢):

shalter@f4-linux:~/halter73/SlowClose$ dotnet run
Hello World!
Delaying 00:00:01.0020110 seconds after receiving 2121024 bytes in 00:00:00.0093720 seconds
Delaying 00:00:01.0255896 seconds after receiving 4283712 bytes in 00:00:01.0170434 seconds
Delaying 00:00:01.0300538 seconds after receiving 6446400 bytes in 00:00:02.0438292 seconds
Delaying 00:00:01.0288262 seconds after receiving 8609088 bytes in 00:00:03.0763068 seconds
Delaying 00:00:01.0296704 seconds after receiving 10771776 bytes in 00:00:04.1067126 seconds
Delaying 00:00:01.0283370 seconds after receiving 12934464 bytes in 00:00:05.1392960 seconds
Delaying 00:00:01.0303644 seconds after receiving 15097152 bytes in 00:00:06.1685186 seconds
Delaying 00:00:01.0303645 seconds after receiving 17259840 bytes in 00:00:07.1997685 seconds
Delaying 00:00:01.0303034 seconds after receiving 19422528 bytes in 00:00:08.2310796 seconds
Delaying 00:00:01.0300118 seconds after receiving 21585216 bytes in 00:00:09.2626212 seconds
Delaying 00:00:01.0278831 seconds after receiving 23747904 bytes in 00:00:10.2959999 seconds
Delaying 00:00:01.0308185 seconds after receiving 25910592 bytes in 00:00:11.3243145 seconds
Shutting down socket.
Shut down socket.
Server read task completed gracefully with 0 bytes read
Server sockets disposed
Delaying 00:00:01.0298779 seconds after receiving 28073280 bytes in 00:00:12.3565051 seconds
Delaying 00:00:01.0000375 seconds after receiving 30170432 bytes in 00:00:13.3863455 seconds
Delaying 00:00:01.0305723 seconds after receiving 32333120 bytes in 00:00:14.3870607 seconds
Read all data