Pulling Up Old Fence Post Broken off Below Ground

Isn't there a tool that grasps on the end of the post, and grips the post tighter the more you pull up on the post? getting those ones that are broken off below ground are a bear, and I swear I've seen a tool like that. Sort of a scissor action.
If you know the name of this gadget, please put it here. Thanks, fellas.

And while we're at it, are there any good vids you can recommend that talk about using a farm jack to do the pulling? Thanks a bunch.

 

If you've got a handy man jack use it. Dig around the post and drop a double half hitched chain over it, the the other end around your jack.

The other deal your thinking of might be this?

American Power Pull - Post Puller 36 (14600), Standard

 

Another subject about like skinning a cat, many options . First you need to use a thin flexible choker or something to grip the broken post stub .Then hooked low on a rear tractor tire, three point hitch, dozer blade or over a block so it pulls straight up on removal .Depends on whet you have to work with .I've used a little Allis model B that was brand new in 1938 .

 

Your description of "scissors action" sounds like a pallet puller.
https://www.google.com/search?q=pallet+grabber&source=lnms&tbm=isch&sa=X&ved=0ahUKEwj697atj5zzAhXQqZ4KHSVyBg8Q_AUICSgC

But....If the stub is wood and the end is tapered or rotted a bit, The pallet puller may just simply slip off.
I would look for the max jaw opening before buying.
Need to be sure it opens far enough to fit the posts.

The choker idea, that others have mentioned above, may very well be the best method.
Choker can likely be adjusted to fit a wider range of things, like concrete around a post stub.