Down here in the South - when winter hits before the tomatoes ripen - instead of throwing them away, putting them in the compost pile or just letting them hang, many use them to make tasty things.  i.e. Fried Green Tomatoes, green tomato relish, pickles, jam, salsa, cake and even pies. 

I know of a fig tree, that usually doesn't ripen all it's figs and am thinking about trying them in something.  I googled uses for unripe figs and got several possibilities.  Have any or you tried any of these?  And yes, I've seen the answers about using them as compost, goat fodder, curdling milk, coating homemade paper, and for removing warts.  I also am aware of the sometimes translation of what an unripe figs represents in the Mishnah!

Baby Fig Spoon Sweet (Sikalaki Gliko)
Unripe Fig Jam
Spiced Green Figs
Unripe Fig Chutney
Greek fig preserve with immature figs and almonds           
Unripe figs boiled in cider vinegar and golden syrup
" Hard, unripe figs are best stewed, then used in cakes, jams, or pickles"
Fig Konfit
Pickled unripe figs