In order to orbit, you have to be outside the photon sphere, which is 3/2 the Schwarzschild radius. It's theoretically possible for the person on the outside to continue holding hands and not fall in, even though the person on the inside will hit the singularity in a finite time. This is because, from the perspective of someone outside the black hole, it takes an infinite amount of time to fall in. It's just that due to time dilation, only a finite amount of time passes.
It will probably be easier to think of it with hyperbolic motion instead of a black hole, since it works with general relativity. You're on a spaceship with constant acceleration. Someone behind you would have to accelerate faster to keep up with you. Suppose your friend falls off the ship, and you grab his hand. Unfortunately, he falls beyond the event horizon. The light that leaves him as he's about to cross it will slowly reach you, but you'll never see him cross it. You'll see him redshift and slow down exponentially. Your hand will also slow down exponentially, so only a finite amount of blood will reach it and come back.
From his point of view, he will quickly pass your event horizon, taking your hand with him. At this point, even if he were to reach the speed of light, he'd stay a finite distance behind you. Except that since you're accelerating, due to lorentz contraction that distance is actually increasing. He will be pulled away from you, and even if he lets go of you, your hand will eventually be pulled from your body.