How to shoot clear fishing line on a white background for extraction

I would suggest "Don't".

Seriously, if the concern is extraction, it becomes much easier if you're free to select your background color. Shoot with an appropriately contrasting background and extract from the colored background. After extraction, the image can be overlayed on any background including white if that's what's required.

Additionally by selecting an interesting color, you can light it such that hints of that color can show in the clear line for additional contrast and interest. If the goal is to emphasize the colorlessness of the line, use a gray background.

The requirement to have the image on a white background does not mean it has to be shot that way.

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Your comment about shadows suggests that you have the product in contact with the background. You may want to suspend the product with the background far enough away to eliminate shadows.

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I didn't have any fishing line handy but I found some old translucent lawn trimmer line in the garage and some nearly invisible transparent thread from my wife. I bundled both up and hung them dangling in front of some black poster board. I placed a single remote flash on a convenient shelf about 30 degrees behind the target as well as using the on-camera flash for front lighting.

I used a quick and dirty color selection for extraction.

White remote flash as shot

White remote flash extracted with black background

White remote flash extracted with white background

Blue remote flash as shot

Blue remote flash extracted with black background

Blue remote flash extracted with white background

I think a white background is going to be a tough proposition!

I'd propose putting dark cards on either side of the fishing line which should help obscure the edges and make them characterized. Where precisely the dark cards would be put relies upon the arrangement you have.

Get a light board that evenly illuminates. Shoot two shots locked off on tripod. One with the light board on. And one with the light board off and subject lights on. This will create a mask that you can use to lift your transparent line out while retaining white looking background. What you need to do is choose the correct exposure when shooting the illuminated light board so you get sufficient contrast between the light board and line. This can be further achieved by moving the line out on a further plane from the light board itself. The further away will allow more negative light in a dark room. You can use clear acrylic to add a solid plane for this.

This is hard to do with indirect light, but you could sub the light board for an evenly lit white backdrop.

The key here is a dark room and distance from the lit backdrop when shooting the mask layer.

Read more about this similar technique in my other post here: https://photo.stackexchange.com/a/65258/41105 The post is about silhouettes, but the same concepts are used to create good transparency masks.

As BobT states. You could probably get away with one shot if you use a second plane that puts the subject out in space from the backdrop. Technically you should be using negative flags for your subject instead of light to define your clear reflective subject (the fishing line). The acrylic plane will accept reflections in a single shot scenario so you will have to get tricky or hang your line. That is why i first suggested mask style double shot.

Happy shooting.