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.
Olive Oil might be the oil... but it would leave one smelling like a salad ;^)>
More likely an animal fat oil of some kind. Wealthier people would have used something commercial.
The Egyptians used unguents made of animal and vegetable fats. It's probable that was what was traded around the Mediterranean area for such purposes. I just saw the Tutankhamun exhibit at the De Young Museam in San Francisco today and Tut had numerous unguent and oil jars buried with him along with unguent applicators.