Certified GKH Gardening Expert
Figs left on the tree are normally the result of unripened fruit. Usually unripened figs are an indication of a possible problem related to stress. You should find out what that might be beforehand in order to alleviate future probelms. Here is an article that you may find helpful: https://www.gardeningknowhow.com/edible/fruits/figs/figs-not-getting-ripe.htm
If the unripened fruit is simply due to excessive fruiting, you can allow them to drop on their own (or let the birds get them). This will not affect the tree. Whatever may be left later on can be pruned off. This article will help with pruning these trees: https://www.gardeningknowhow.com/edible/fruits/figs/pruning-fig-trees.htm