It is very possible that your trees sustained a winter injury. Were the trees wrapped/covered during winter? I would recommend giving your trees a scratch test per the guidelines in the following article: http://www.starkbros.com/growing-guide/article/how-to-do-a-scratch-test/. A scratch test will help determine if your tree is still alive and what limbs are genuinely dead. With a scratch test, "green is good" and means there is hope of recovery. If a scratch test on a trunk of a fig shows no sign of life, I would wait several weeks (just to be sure) and if nothing changes then I would cut that tree down to the base and hope that the roots, which are likely still alive in the ground, will send up new shoots this summer. If the scratch test reveals life-less branches, you will want to prune those dead branches away. For more information on pruning fig trees, please visit the following link:
https://www.gardeningknowhow.com/edible/fruits/figs/pruning-fig-trees.htm
And, from this point forward, I would make sure that you take measures to protect your fig trees in the winter. Guidelines on how to do so can be found here:
https://www.gardeningknowhow.com/edible/fruits/figs/fig-cold-protection.htm
In addition, here is an article that will help you which further discusses leafing out problems on trees and how to diagnose them:
https://www.gardeningknowhow.com/ornamental/trees/tgen/tree-leafing-problems.htm
