Alright - the best way (I think), is to make a front & back closed curve, with a middle curve that's larger/wider in order to produce a ROUNDED edge in the final stage.

I have a rectangle on the top, followed by a wider 'odd' shaped closed curve below it, followed by a smaller one below that -

Then LOFT.

Set the loft to a high number in order to create a tight wire frame.

Remove the loft SURFACE so it looks like a WIRE FRAME EXTRACT.

Remove the middle curve (the larges one in the middle - you've already got the curve you wanted - it's served it's purpose).

Now you have a closed curve at each end of the ribs which the LOFT created -

Select the TOP & BOTTOM curve - Select the side curves (ribs), and create a NETWORK CURVE surface.

That will result in a nice curved wrap-around surface for the purpose of FLOW ON SURFACE, and the FRONT & BACK are open.

We want the front to be open, however, we want the back to be closed!

How would that be possible?

I can't post the design -

My goal is to have ONE WHOLE NETWORK SURFACE for the purpose of FLOW ON SURFACE in which there is only ONE HOLE, (at the top) and everything else is wrapped & closed - the difficulty is you can't JOIN two Network Surfaces and make them into one -

I want to be able to FLOW on SURFACE as though it were one continuous surface for the purpose of 3d texture - that would continously wrap all around the object, including the edges on the front - up to the HOLE - and down around the curved sides and continue to cover the entire bottom of the object - where, there is now - a hole - is it possible to make a CURVE NETWORK that has only ONE HOLE (which happens to be at the top)?
Cheers,
Cash Me Outside