On my cherry trees, I have wrapped plastic food wrap around the trunk, somewhere where the bark is fairly smooth. Over the plastic wrap I smear a band of grease about an inch and a half wide, so there is no way up the tree for the ants without crossing the grease. I'm not sure that the tree would like the grease straight onto the bark. If the bark is not smooth sometimes the ants find a way under the wrap. Tanglefoot can be used instead of grease. I have had ants eat my figs, but never a real problem.

David

Tanglefoot stops the ants i use this. The yellow jackets can be fierce and seem to tell the friends when they find something and before you know i you have so many and this sounds like what your going through.
It happened to me and the culprit was my pussy willow tree they were attracted to it, that winter a storm split it real bad and i cut it down. Now i get the occasional yellow jacket here and there and any fallen figs must be picked up as this will attract them as well. Watch if they have a nearby area in my case this year they were going into 1 of my chainlink fence pipes (gate posts) and that was taken care of. Also had to spray a nest in corner roof of shed as they were there as well which is near the trees.
In short anywhere you see them gathering in a pipe, fence, corner of roof etc you would have to get them outta there.
Another option is to buy or build some homemade wasp trap these will capture many as well but keep them away from your fig trees not to attract them there in that area.
I still get some yellow jackets here and there and shoe them away with my hat i wear but nothing close to the many before.
You will never get rid of them just manage there numbers hopefuly.
Martin

Yellow jacket traps work well. A fine netting would keep them off the fruit.

The plus for them is that they are bug eaters. The minus is that they are aggressive about stinging, so I get rid of yellow jacket nests. The other hornets I leave alone unless they are getting into the house or decide to get territorial about the fruit.

One option is to harvest after dark when they are in bed. So what if the neighbors doubt your sanity as you are out there with a flashlight picking figs?