I think this, like most things taiji, is misunderstood both in terminology and in application by quite a few. My teacher had me fajin him vs. fajin a pillar supporting a beam in his practice room, by way of explaining the difference hands on. Yes, of course you can fajin without an opponent, who's to stop you if you have the know-how. And no, that pillar didn't give me anything to use against it, I could only rely on my very own resources. Whereas a live opponent is going to give you something you can appropriate and turn against him (if you have the know-how of course.) Don't use your own resources is the golden rule of good push-hands.
The highly skilled practitioner won't give you anything though. Moreover, they will create a perfect sensory illusion of "nothing there" -- try using fajin against a cloud, a swath of fog, a tactile emptiness... Very educational. So that pillar does give you something after all -- its own hardness which it is unable to soften, let alone to the point of disappearing from all your senses except your eyesight.
Are you familiar with the "bu fa" technique?