Un-close pasted path

I've got a pattern of abstract paths in Photoshop that I've pasted into Illustrator. So far so good. However, both programs have a habit of automatically closing shapes.

 In Illustrator, the shape (see bleow) is automatically closed (whereas the left hand side should be open).

In order to fix this I'm currently having to locate each shape, direct selection of each point, cut it, paste it in place and then re-apply stroke to it. Like the shape as I want it!

This process is fine for a couple, but really rather long winded for hundreds of shapes. 

Is there an easy/faster/better/cheaper way of solving this? What have I missed?

As always, answers on a postcard...