I force my in-ground figs into dormancy by cutting off their irrigation. I don't know if that's a good idea or not, but I've always done it to try to minimize frost damage, so they're not actively growing when it gets cold. When the leaves on the brown Turkey drop off, there are always numerous partially-developed figs left hanging on the branches. I usually pluck them off once they dry out, although I know of no real reason to do so.
This year, since the BT seems to have insurmountable souring problems due to a beetle infestation, I'm going to let it keep growing and see what happens. I'm curious to find out whether the figs will have time to ripen, and if they do, whether they will even be any good since the days won't be very hot. I figure I'll lose the current year's growth to frost damage, but I was planning to prune it back anyway--so that's okay.