using System;
using System.Collections.Generic;
using System.IO.Ports;
using System.Text;
using System.Threading;

namespace AsyncReceiver
{
    class Program
    {
        const byte STX = 0x02;
        const byte ETX = 0x03;
        const byte ACK = 0x06;
        const byte NAK = 0x15;
        static ManualResetEvent terminateService = new ManualResetEvent(false);
        static readonly object eventLock = new object();
        static List<byte> unprocessedBuffer = null;

        static void Main(string[] args)
        {
            try
            {
                var serialPort = new SerialPort("COM11", 9600, Parity.Even, 8, StopBits.One);
                serialPort.DataReceived += DataReceivedHandler;
                serialPort.ErrorReceived += ErrorReceivedHandler;
                serialPort.Open();
                terminateService.WaitOne();
                serialPort.Close();
            }
            catch (Exception e)
            {
                Console.WriteLine("Exception occurred: {0}", e.Message);
            }
            Console.ReadKey();
        }

        static void DataReceivedHandler(object sender, SerialDataReceivedEventArgs e)
        {
            lock (eventLock)
            {
                byte[] buffer = new byte[4096];
                switch (e.EventType)
                {
                    case SerialData.Chars:
                        var port = (SerialPort)sender;
                        int bytesToRead = port.BytesToRead;
                        if (bytesToRead > buffer.Length)
                            Array.Resize(ref buffer, bytesToRead);
                        int bytesRead = port.Read(buffer, 0, bytesToRead);
                        ProcessBuffer(buffer, bytesRead);
                        break;
                    case SerialData.Eof:
                        terminateService.Set();
                        break;
                }
            }
        }
        static void ErrorReceivedHandler(object sender, SerialErrorReceivedEventArgs e)
        {
            lock (eventLock)
                if (e.EventType == SerialError.TXFull)
                {
                    Console.WriteLine("Error: TXFull. Can't handle this!");
                    terminateService.Set();
                }
                else
                {
                    Console.WriteLine("Error: {0}. Resetting everything", e.EventType);
                    var port = (SerialPort)sender;
                    port.DiscardInBuffer();
                    port.DiscardOutBuffer();
                    unprocessedBuffer = null;
                    port.Write(new byte[] { NAK }, 0, 1);
                }
        }

        static void ProcessBuffer(byte[] buffer, int length)
        {
            List<byte> message = unprocessedBuffer;
            for (int i = 0; i < length; i++)
                if (buffer[i] == ETX)
                {
                    if (message != null)
                    {
                        Console.WriteLine("MessageReceived: {0}", 
                            Encoding.ASCII.GetString(message.ToArray()));
                        message = null;
                    }
                }
                else if (buffer[i] == STX)
                    message = null;
                else if (message != null)
                    message.Add(buffer[i]);
            unprocessedBuffer = message;
        }
    }
}

This program waits for messages enclosed in STX and ETX bytes and outputs the text coming between them. Everything else is discarded. On write buffer overflow it stops. On other errors it reset input and output buffers and waits for further messages.

The code illustrates: