Coyote or maybe fox. Jon is right, possums teeth are too sharp. It looked like the chips wasps take out but for the symmetry that identifies it as teeth.

The matching marks on both sides of the fig, which I can't seem to photograph clearly, do indicate an animals teeth .
Maybe these pics are clearer.
Seems like an animal would just take it away. Perhaps the others eaten in place , not removed from the bush, were slugs etc.

Forgot to mention the widest part of the bite mark measures about .75"

Oh! well, that's a baby Chupacabra then...

It was really puzzling me, so I did a web search.  No self respecting opportunistic coyote on this earth would NOT eat the whole thing! They eat ANYTHING from rodents to vegetables to fruits.  I doubt they would leave a trace.   A 3/4" tooth mark means something big.  

I was thinking Bats, but it has to be something much bigger.  Even my teeth aren't that big!  What could it be?  I don't think slugs have teeth.

Suzi

Suzi , I meant to say 3/4" width of bite mark. So something sort of little I think.
Alexis , perhaps the Chupacabra family is summering in the NH lakes region and the baby came along ? I thought they hunted in PR for the most part , but maybe they rode north on some Javelinas.

Yep. Global warming.

bug marks, stick to that. If it was an animal, and the teeth marks are that big, it would have swallowed it whole. I don't know if bugs have teeth, but this is bug damage.

luke

I had some "damage" to my brown turkey,,,, it started on friday,,, holes pecked all through it,,,, a few more were almostttttt ripe so I left them. He got another one yesterday morning,,,, this morning I went out and there was the last one ,,,, all chewed up, grrrr. This time though he left a calling card,,, a bright red feather sitting on one of the branches,,,,, It's a cardinal  judging from the feather,,,, I USED to like cardinals,,, now I'm at war with the bastid!  Hitting home depot in a few minutes to get some netting, ugh.

Kerry, have you noticed any bees around your figs?  I've had similar damage by both yellow and Black bees. The black bees did a job likke I've never seen before. At first glance the dark figs looked like they were covered with black ants that wouldn't brush off. Closer observation I watched black bees eating. The puckered up the skin and ate the insides. The yellow bees ate holes similar to what your picture shows.

Just a thought, good luck in finding an answer,

Peg, zone 6, CT

Haven't seen any bees or wasps, etc. around any of my figs , but I am sure I could have missed some.
I would like to think it is insects rather than animals, but the almost identical marks on opposing sides of the fig look like a perfect picture of an unfinished bite. But I will keep my eyes peeled for bugs as well.
I am stumped at this point.
Time to pull out the clam shell package I saved

Once I did witness a few young (1/2 sized) pillbugs feasting on some semi-ripe fig skins.
It was in the early wee hours of one damp morning.
The skin 'scars' left were very similar...