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It is hard to say what kind of borer, as there are several that can attack figs, and you can only identify it if you see it. This article covers several kinds of borers and recommends treatments:
https://extension.missouri.edu/p/g7190

Figs need about 3-6 years to reach maturity and be able to fruit. You may just need to wait a little longer to get fruit. This article will help as well:
https://www.gardeningknowhow.com/edible/fruits/figs/fig-tree-is-producing-fruit.htm

Your fig may also have died back some. If the branches are still pliable, the branch is still alive and will leaf out. If it is brittle, it is dean and will not. But even if the branches are dead, figs often regrow from the roots, so look for that as well.

You can grow figs there. When you plant them, make sure that you backfill the hole with good topsoil, instead of the sandy soil. I would also make sure that you add some topsoil or mulch (that will become soil) a few feet around the trees. This will eventually work its way into the sandy soil. You may also need to water a bit more than usual, depending on how fast the trees grow.

Figs take about 3 year to fruit when grown from a cutting. Sometimes sooner, but that is the average.

This winter was particularly cold for most of the U.S. It is possible that it simply got too cold or was caught in a late cold snap. If the stems are still alive, it will regrow its leaves. If the stems are dead, but the roots are alive, it will regrow from the root. This article will help:
https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm

Perhaps, this article will help in the future: https://www.gardeningknowhow.com/edible/fruits/figs/fig-cold-protection.htm

For now, you'll just have to wait. As long as the stems are still alive, the leaves will regrow. This article will help determine if the tree is still alive: https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm

It was a very cold winter this year, and they may have died, especially if the branches are soft and black, which indicates cold damage. However, figs can grow back from the roots, if the roots survived. Check the roots to see if they are still healthy. If they are, give the tree some time to sprout. You may find this article helpful:
https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm