I live 15 miles North of Springfield, MO, which is about 500 miles SW of Chicago. I planted two Chicago Hardy Figs. The fig that's against the foundation of the house dies back to the root every Fall and grows back every Summer; the figs never ripen before die back. The other fig died.
I posed this same question on the old forum and no one indicated that deer ate figs, though it was my guess that they would, since deer like sweet fruit.