A few times I used a long joist 6 x 2 as a lever with the post stub attached to it with rope a foot or so from the end....a few offuts of joist under the end of the lever to stop it sinking into the soil. A lot depends on how much concrete is in there, amateurs usually make their post holes far too big and theres like a 1/4 ton of concrete in there....
I like Red's come along idea (cargo ratchet straps are great for tensioning fence wire too) You could have a strong frame, like a sawhorse, but higher and stronger built, with a bigger gap underneath. Then set it above the dead post and use a ratchet strap to haul it out, using the grab hooks to reach under for ones where the post has rotted out? They do have some strong pulling power
