I have this fig tree that, while the trunk didn't make the winter, it has little, new trees growing around it (little trees not shown, this picture was taken in the spring).

The little trees are about 1-2 feet high. 

I want to save them - how to I do that?  Should I dig around it and put in a pot, and put in the garage over the winter?   Any special digging instructions?

Also, is now the time to dig up, or should I wait?  I'm in NJ.  

Is leaving it in the ground even an option?

Scratch the bark and see if there is any green underneath. The large trunk looks alive. The rest look dead.

Hi,
With a recent pic it would be easier.
What I would do is pull some trees with roots, pot them, and when they are dormant, put them in a garage or cold basement.
Leave the rest of the root-shoots outside and protect them the best you can.

You could air layer some of the live stems if you think the weather will hold 4 more weeks.  You could and probably should take cuttings to root.  You could heavily mulch the whole plant and expect it to die back to the ground every winter.  If it doesn't come back and produce figs, though, then there's no point in leaving it in ground.  You should wait until the plant goes dormant before digging it out.