Servidor de bate-papo multithreading em C #, identificador de desconexão

Estou procurando uma maneira de lidar com uma desconexão, porque toda vez que fecho um cliente, o servidor para de funcionar. Recebo uma mensagem de erro de que "não é possível ler além do final do fluxo" nesta linha:

string message = reader.ReadString();

Também preciso de uma maneira de excluir o cliente desconectado da lista de clientes. Aqui está o meu código: Servidor

using System;
using System.Threading;
using System.Net.Sockets;
using System.IO;
using System.Net;
using System.Collections.Generic;

namespace Server
{
    class Server
    {
    public static List<TcpClient> clients = new List<TcpClient>();

    static void Main(string[] args)
    {
        IPAddress ip = IPAddress.Parse("127.0.0.1");
        TcpListener ServerSocket = new TcpListener(ip, 14000);
        ServerSocket.Start();

        Console.WriteLine("Server started.");
        while (true)
        {
            TcpClient clientSocket = ServerSocket.AcceptTcpClient();
            clients.Add(clientSocket);
            handleClient client = new handleClient();
            client.startClient(clientSocket);
        }
    }
}

public class handleClient
{
    TcpClient clientSocket;
    public void startClient(TcpClient inClientSocket)
    {
        this.clientSocket = inClientSocket;
        Thread ctThread = new Thread(Chat);
        ctThread.Start();
    }

    private void Chat()
    {
        while (true)
        {
            BinaryReader reader = new BinaryReader(clientSocket.GetStream());
            while (true)
            {
                string message = reader.ReadString();
                foreach (var client in Server.clients)
                {
                    BinaryWriter writer = new BinaryWriter(client.GetStream());
                    writer.Write(message);
                }
            }
        }
    }
}
}

Cliente

using System;
using System.Net.Sockets;
using System.IO;
using System.Threading;

namespace Client
{
   class Client
   {
       public static void Write()
       {
        TcpClient client = new TcpClient("127.0.0.1", 14000);
        while (true)
        {
            string str = Console.ReadLine();
            BinaryWriter writer = new BinaryWriter(client.GetStream());
            writer.Write(str);
        }
    }

    public static void Read()
    {
        TcpClient client = new TcpClient("127.0.0.1", 14000);
        while (true)
        {
            BinaryReader reader = new BinaryReader(client.GetStream());
            Console.WriteLine(reader.ReadString());
        }
    }

    static void Main(string[] args)
    {
        Thread Thread = new Thread(Write);
        Thread Thread2 = new Thread(Read);
        Thread.Start();
        Thread2.Start();
    }
}
}