I would make sure that the fig cutting have not froze. I have never stored fig cuttings. Since I have a greenhouse, I normally just put them in a soilless mix to begin the rooting. Same with blackberry.
You can store cutting in the crisper of your refrigerator in a sealed ziploc bag. Put a paper towel in with the cutting that has been misted with water. Just don't soak it. You want just enough moisture to keep the cuttings from drying out but not wet enough to develop mold.
Someone has a greenhouse they haven't spoke of lol... Someone should be spending more time in this section with the knowledge they have..