And similar in case of a black hole, you are falling through the event horizon and nothing happens, it is just that calculating what you need to do to escape, you note that it is too late.
To expand a bit on the molecule situation, when one of the atoms is inside the black hole, then parts of its electric field are still outside and influence the other atom. To have the other atom escape to infinity, you would need to break the part of the bond "still outside" and the gravity of the black hole.
You know how the universe is expanding, such that the milky way is moving away from (sufficiently) distant galaxies faster than the speed of light? But chemistry still works fine here? When you fall into a black hole, you accelerate until you're moving away from the rest of the universe faster than light, but all your atoms are still (relatively, assuming the black hole is large enough to have negligible tidal forces) stationary relative to each other. The event horizon is just the point where your speed relative to the effectively-distant[0] outside universe exceeds the speed of light. Any signal you emit can't be moving facter than c relative to you, so it will always be moving away from the outside universe (v<-c implies v+v'<0).
0: "Nothing can move facter than c" refers to relative motion of objects near each other, which is why the Hubble expansion of the universe doesn't contradict that either.
There is a classic analogy of light traveling through space-time being like ants crawling on a balloon. A black hole is a spot where the balloon is being sucked in. Faster and faster as you get closer. The event horizon is where the speed at which the balloon moves matches the speed of the ant. There is nothing special from the ant's immediate perception about this line, but if the ant crosses, it is doomed.