Treat database field as a flat file source
My first inclination would be to use a script component (e.g. C#) as source in a Data Flow Task.  The script would just read the column contents, parse the individual records and fields, and send records down the pipeline.  The individual fields (perhaps strongly-typed) can be defined in the output record definition of the designer.

https://msdn.microsoft.com/en-us/library/ms136060.aspx contains an example of parsing a CSV file and processing a SQL query.  You can combine the two examples for your needs.  Below is an example of this. I don't have time to test right now but it should get you started. 

public class ScriptMain:
    UserComponent

{
    IDTSConnectionManager100 connMgr;
    SqlConnection sqlConn;
    SqlDataReader sqlReader;

    public override void AcquireConnections(object Transaction)
    {
        connMgr = this.Connections.MyADONETConnection;
        sqlConn = (SqlConnection)connMgr.AcquireConnection(null);

    }

    public override void PreExecute()
    {

        SqlCommand cmd = new SqlCommand("SELECT CsvContents FROM dbo.CsvImportTable;", sqlConn);
        sqlReader = cmd.ExecuteReader();

    }

    public override void CreateNewOutputRows()
    {

        while (sqlReader.Read())
        {
            {
                string csvContents = sqlReader.GetString(0);
                CreateNewOutputRowsFromCsv(csvContents);
            }
        }

    }

    public void CreateNewOutputRowsFromCsv(string csvContents)
    {

        string nextLine;
        string[] columns;

        char[] delimiters;
        delimiters = ",".ToCharArray();

        nextLine = textReader.ReadLine();
        while (nextLine != null)
        {
            columns = nextLine.Split(delimiters);
            {
                MyAddressOutputBuffer.AddRow();
                MyAddressOutputBuffer.AddressID = columns[0];
                MyAddressOutputBuffer.City = columns[3];
            }
            nextLine = textReader.ReadLine();
        }

    }

    public override void PostExecute()
    {

        sqlReader.Close();

    }

    public override void ReleaseConnections()
    {

        connMgr.ReleaseConnection(sqlConn);

    }

}