I have a perlite rooting chamber that I am growing cuttings from my own figs in and other plants (and doing well), and I stuck some mail ordered fig cuttings in there as well when I received them. Dipped in rooting hormone powder.
They do not seem to be doing well at all and today I’ve thrown 3 of them out. The ends were mushy and I could not cut enough material away to see nice clean wood.
Here is a cross section of one that still scratches green on top but looks done for on account of that brown ring.
Should I toss them all, or can this turn the other way if I give them more time? I’m sad to be out forty bucks but I don’t want to prolong and let things get moldier. 
PS: This is after I cut off the bottom 1.5" on account of it rotting in the perlite. There is a heat mat underneath and I do spray with Physan 20 daily, but I did not dip them in bleach when I received and perhaps I should have. Although my home-collected cuttings are unfazed by a little mold…
Are the buds in good shape? Grafting might give you a better chance. It looks like half of the cambium is still good, sounds like they might have gotten frozen or something.
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Thanks Hoosier you are giving me hope 
I have cut the bottom rot off the other cuttings and noticed that one of them had lenticels forming (that beginning white roughness before roots) so I have tentatively laid them on their sides shallowly in the perlite.
This looks too thick to graft, right? My fig grafting success has been with more succulent young tips. This seems too large to chip graft, but maybe a cleft. The buds don’t scream “graft me” but my experience is limited.
Green line is where I cut the piece. And I have pretty average sized hands.
Can you dig up roots to graft on? You could do a whip with a thick root, the bark layer is a little thicker on roots so it would need to be a little bigger than the scion. Thinner roots can be clefted or maybe veneered.
How long have they been rooting? That powdered rooting hormone used to have a bad reputation when i started growing figs. Did you use it on the other cuttings as well?