I doubt very much if it's any variety that could not be found in any common, garden center...so, no gormet-type figs. The gardeners probably picked up that tree when they went to go get another fresh load of manure.
My guess: "Brown Turkey"...or..."Celeste". One produces large delicious-looking fruit, tastes like crap... and, always disappoints. The other produces plenty of promising fruit, but drops them at the last minute. Both should be swapped for a better variety.
I agree with post #16. I wouldn't "buy" anything she's selling. Nice K-Mart outfit.
Frank