Joe, as long as I keep the irrigation turned on they will stay green up to the first frost--but if temps dip much below freezing, they get hammered. So, I usually force dormancy by cutting the water to my in-ground figs sometime in late September. The potted ones keep getting watered--I haul them into the garage whenever there's a freeze warning, and then back out again, but they still end up dropping their leaves later in the winter.
My in-ground BT is always still loaded with figs in fall when I cut the water. Last year I decided to keep watering it just to see if any would ripen, and several did--but it wasn't worth the trouble, and the tree was heavily damaged during that hard freeze (it probably would have been anyway, since it got so cold). I'm just confused about the issue of how long to leave unripe figs on very young trees in our climate. I hadn't considered it an issue, but maybe it is. So, unless I hear otherwise, I'll probably follow Pete's advice and at the end of September strip off anything that clearly can't ripen in the next 3-4 weeks.