88 ford taurus

My daughter owns a 88 ford taurus. It has over 200,000 miles on it.
It belonged to my grandmother who can't drive any more.
She has never had any trouble with it.
However last night my daughter was driving home when she noticed the smell of oil. Transmission oil as it turns out.
She stopped the car and shut it off.When I got there it looked like oil was dripping from above the oil pan the oil smells burnt. I checked the dipstick and found no oil on it. She says it was shifting funny throughout the day.
I checked the oil in the tranny early in the afternoon before this happened the level was fine.
Today I put it on jack stands and took a look could'nt find the leak.
So I added 6 quarts of transmission fluid and a can of conditioner.
We drove around for about 25 minutes. No leaks .She went to my parents tonight [thirty minute drive] she said the engine rpms raced once other than that it was fine .
Could the oil have boiled out? My father picked the car up the night before on his trailer he said there was a four inch wide oil slick on the road about 400 yards back. All the way to where she stopped.
Should I change the variable speed sensor?
This whole thing has me puzzled.
How could the oil get out of the transmission?

Um...a leak.

Many times leaks won't be active if the engine is off.

Years ago I took a car to a AAMCO transmission shop. They told me where the leak was coming from for free.

Don't start replacing parts that sound important. Make sure you replace the right one the first time.