I'd say that depends on the size and structure of the tree. Dividing a single fig with a backhoe, without making a real mess, seems like a challenge though.

Fig trees are not grafted onto any rootstock and are not like most other fruit trees. So, you can take any sprouts that emerge around the base of the mother tree that come from below the soil line. These sprouts will produce the same kind of figs as the mother. Many sprouts will have roots on them and these can easily be taken with a shovel. Try to cut into the mother tree when you dig up the sprout. This is imporant if the sprout does not contain many roots. Then plant them in some good potting soil and they should finish rooting for you in no time.