One workaround that immediately comes to mind is to modify your activex script task to insert a dummy row into each of the empty text files and then after the data pump tasks do a clean up step (SQL Task) to delete the dummy rows that have been inserted.
Aside from that I would need to see the script and a brief run down of your package.
David Lundell
Principal Consultant and Trainer
www.mutuallybeneficial.com