I very carefully cleaned the mulch away from my one in ground fig yesterday and found one little green sprout. Hip-hip-hurrah! You can just see it here at the base of the one stem that looks wet for about four inches up.
  That is far from all the stems, but it's the only one that looks wet like that. And it kept looking like that all afternoon and still this morning. I broke off all the dry brittle growth, all those stems are still flexible, but the only one sprouting is the one that looks wet. Is a stem looking wet an indicator of life in figs? I haven't seen it mentioned anywhere.

Congratulations on the sprouting.  I can't tell you anything about the wet stem.

Hi Greysmith,
To my experience, it looks like frost damage. The tree is pushing the sap but the sap does not go through to the top of the tree, so it leaks ...
Wait and see - but to me that stem is dead .
I would monitor the roots at that stem and check that they don't rot due to stagnating water. And if they do rot, I would remove the roting material .

Has it dried out since your post ?

Yes, it did dry late yesterday but there was a wet spot this morning about half way up what had been wet and on the other side from the sprout. I've spotted another sprout at the base of another stem. We have more weather coming. rain Wed., then cooling. They're calling for mid forties but I'm betting on it getting into the thirties here. Going to do what I can to keep it dry and warm.

Check for borer holes. A wet spot like that is why I looked closely enough to spot them on my trees.