It occurred to me that mending this would present parallels to vascular surgery and so I made these initial notes on examining it:
Mending Delicate Fabrics:
Prepare sequence of mending after assessment-washing, shaping, reassessing.
Tiny details almost invisible to the human eye which we disregard,detail was once more important and readable as a language of stitch.
Hand work that now looks to us like machine work so we don't believe it.
Tiny stitches in very fine fabric but no distortion from the needle despite heavy thread.
Raw edge to the cotton itself but so many embroidery stitches that finishing is unnecessary to stabilise the edge.
After gently damping the collar with a wet cloth,(not submerging in water because the weight of water could be damaging) I carefully reshaped it onto a thick towel. It was not the asymmetric design I had thought but a symmetrical one that had lost a part.The true shape was now revealed as rhomboid with an elliptical centre ,the lace still limply edging the whole. Once carefully ironed the original nature of the collar emerged as a 4D shape rather like a mesentery (organ of the digestive system) .....all frilly!!
It is only after these observations that the job of mending the tear was the focus.