The old timers used to put a drop of an edible oil in the eye of a fig to hasten ripening.  Would this stop the ants?  I ask because se hear so much about it.  Tanglefoot works well to keep the ants from climbing the trunk but perhaps these are getting in some other way.

I just eat them with fig... lol

I heard tanglefoot will help prevent them getting to the figs and stop them getting away.

I have seen and tried using the medical breathable tape or maybe even those round bandaids.

Pete, you're getting a balanced meal with the extra protein lol, but I'm thinking not everyone shares your gustatory style. Tanglefoot should definitely work Maybe there are branches touching up against another tree and they are climbing up that one to get to the figs. Look for the trail of ants to the figs and follow it to the ground, then you can prevent with tangle foot or simply moving the fig away from adjacent trees if they are climbing up them. That should resolve it for you. 

And why does a drop of oil hasten ripening? Does this hasten ripening affect the taste?

Google:  tanglefoot.

100% effective, pesticide free, safe for trees.

Tanglefoot works been useing it for some years now.

If you grow in bush type then i can see it being a pain to use as you would have apply to each trunk to prevent the ants journey up the tree.