Probably laying on top of the burlap (which is attached to the springs) but in either case, it should be hog-ringed to the springs to keep it from moving around.
You are right on hog ringing it in place,and here is a good tip for sagging springs.
If you have a old couch or chair you are trashing,pull the springs from it.You can bend them into the shape of your old spring and use them as replacements,they are a bigger diameter than the automotive springs.Kinda of a pain in the rear to bend,but will firm up a seat real good.