Instead of a search for info on pruning fig trees you should have done a search on ROOT PRUNING because there is a copious amount of information on the subject. To the point where most people will not even post in a thread about it because the subject has been talked to death. So everyone assumes the person asking did not really look.

If you go to the bottom of the Fig Forum page and type in ROOT PRUNING you will find lots of lots of information on the subject.

You could also click on the link and watch a good video on root pruning. No need to have all the tools and sealers recommended by the person doing the video. Just pay attention to what they are doing and do it to your tree with whatever sharp and clean pruning tools you have.

The basic rules I would follow would be;

while the tree is dormant

Bareroot the tree.

Cut any circling roots or girdling roots and large roots that cross other roots. Cut any broken or damaged or diseased roots. Cut the entire root system back 25-35 percent.

Here is a link that might be useful: Root Pruning Japanese Maple Container Gardens with Tricia Smyth