Keep Illustrator Path Divide Below from Closing Lines

Question

So I have some objects, open-ended lines, and a box:

I select the box and choose Object > Path > Divide Objects Below, and get this:

You can basically see that the objects have been divided, but also made into a closed shape. Even the lines that fell fully inside the box have this happen!

Is there any way to avoid that? So my "lines" are just divided but not closed off?

Or is there a better way? What I really want is to chop the lines where they cross the box. I don't use a Clipping Mask because a) it doesn't get rid of the clipped data and b) I have 30 layers and they all get moved into a single layer

Similarly, I looked at using Pathfinder Crop, but that too creates the closed shapes and also drops everything onto the same layer as a group.

Sorry if my terminology is off. I'm from a GIS/CAD background. Fairly new at Illustrator and frustrated that what should be a simple clip/crop task has taken me two hours to just get this far!!!

Answer 1

You could stroke the open lines, outline the strokes to create thin closed paths, and then do the divide and delete the outside pieces of the lines/paths.

A more freeform method would be to use the Eraser tool. Hold Alt and draw a box with it over the areas that you want to erase, and the paths will be truncated.

Answer 2

Pathfinder commands won't work on lines or strokes. You must have closed paths/shapes for the commands to work properly.

Once you close up your paths the crop command should work nicely.

There will be no way to get around having the shapes move to one layer unless you crop each shape on it's parent layer.