It will depend on the fig.  If they are really ripe and sweet than they will probably be a little sticky from the natural sugars in the figs.  I would look for moisture pockets and continue drying until they are leathery.  If you like them on the chewy side, they might not be quite dry enough to store are room temperature but storing in the freezer is a great option.  You can continue drying or just take out what you want to eat and enjoy and then continue storing in the freezer.  

I love my prunes a little on the soft side but store them in the freezer and just thaw out what I like to eat.  Works great.  If you want to store at room temperature, they need to be completely dry or they will mold.  

Another advantage of storing your dried food in the freezer is that you won't have insect problems.  They love dried fruits.  

Thanks for using Ask Extension

Nellie Oehler