Yes... the mostly undone queue that runs down the back of the neck and onto the shoulders of the image on the Man on the Shroud is slightly blurred compared to other image areas and hair images, probably because of the oils exuding from the queue onto the cloth. Any oil that was there has long since evaporated.
Thinking of what type of oil would be involved.
If a hydrocarbon oil, that would indeed literally evaporate after so much time. The rate is slow after the carbon count goes over a couple dozen, but it’s not as though this happened yesterday.
If something like olive oil or seed oils, perhaps biodegradation by microbes eventually took care of it.