Is there any hope for this if I take it out, unwrap the parafilm, wash in bleach?
It was such a nice stick too I wonder what went wrong! I am using the same cup-in-cup mini-self-watering container and have done great with other twigs from the same batch...

     

It doesn't look good but you have nothing to lose by giving it a try. Is it possible there is still a living node or two at the bottom that could be salvaged if you cut off parts that are too decayed to salvage? 

I had ones in plastic bags with paper towels that looked significantly worse than this and eventually rooted. They were covered in mold. I wouldn't give up

Luigi
That is an interesting rooting method.  Is that outlined somewhere? 

The brown/red at the tip usually indicates rot.  You need to get rid of that. 
I would unwrap the cutting, cut the brown ends off until I reach wood that has green cambium and white pith no brown/red blotches from either end.   If all you have left 1 one good bud that is still enough.  I actually find odds and ends pieces of cuttings root faster although they don't have as much stored energy. 
Then as you indicated wash in bleach and try rooting again in a different soil mix. 
I would try 100% sifted perlite so there is less chance of mold spores. 
Good luck!

Hi Pino,
I am a HUGE proponate of self-watering containers and decided to try it for my fig twigs as well. (Now before trying this method I did try Rich's perlite method. I didn't get how it was to work - perlite doesn't hold water like vermiculite does. I think those twigs never rooted because there was not enough moisture?_

Anyways, these sticks started showing a sign of life on 5/12 and here is what they look like today. This last week was cold and rainy here but I'm thinking the should start experiencing the outdoors soon...I still have some twigs in the fridge. I'm wondering if I should try this setup but have it sit outdoors. 
This is my 2nd year of having a real garden (tomatoes, etc.) and 2nd year of starting things from seed. I have to say that I feel things I've started indoors, in a 'controlled' environment, seem to do better for me than seeds I've tried to start outdoors. So I'm wondering if I should just stick to trying to start these sticks indoors instead even though our weather is getting warm enough now..

 
 

Sorry, I didn't finish answering your question, Pino.
Here are some threads on here that have been specifically talking about mini SIP setups for twigs.

http://figs4funforum.websitetoolbox.com/post/propagation-method-that-is-working-well-for-me-this-year-7306462?pid=1286276578#post1286276578
http://figs4funforum.websitetoolbox.com/post?id=6416006&trail=50

Luigi
looks like you are having good success with your mini-sip!
Thanks for the link.

The top part is definitely dead.  Can't tell about what's under the soil.  Likely it's dead too.  Bleach won't help. 

I think I might have an extra Salce that I rooted over the winter if you are interested.