Quantum entanglement (one particle destroyed) Two particles are experiencing "quantum entanglement". What happens to one particle if the other is destroyed (i.e. falls into a black hole and reaches singularity)? Would the remaining particle be destroyed? In what way would the remaining particle be affected?
 A: The delay time for a particle falling into a Schwarzschild black hole is
$$
cT~=~r~-~2m~ln(r~-~2m),~m~=~GM/c^2,
$$
which diverges for $r~\rightarrow~2m$. It takes an infinite time to observe a particle reach the event horizon. So for an eternal black hole, the mathematical solution corresponding to Einstein's field equations, you would observe your partner with the EPR pair never reach the black hole, and in principle your entanglement is conserved. There would be no loss of entanglement.
This is for a perfect situation that ignores Hawking radiation and the influx of other quanta into the black hole. The physical situation is more messy. First off other quantum fields pile up near the horizon, and in fact the holographic screen or stretched horizon a Planck length or string length above the mathematical horizon at $r~=~2m$ is composed of all the quantum fields that make the black hole. The other EPR pair becomes also a component of the black hole. From the perspective of the distant external observer the other EPR pair interacts with lots of quantum fields and the entanglement phase is lost to the black hole. This is a form of decoherence. After a long period to time watching the EPR pair creep ever closer to the black hole the entanglement is lost to this large reservoir of states. 
You never witness the other particle reach the singularity. That state of affairs is only accessible to an observer that falls in with the particle.
A: Nothing happens.
If something measurable did happen to the partner, and it was due to the entanglement, that would falsify the no-communication theorem (well... one of its assumptions). Basically we'd have to rethink this whole quantum mechanics thing and hand out a bucket of Nobel prizes.
(That being said, if I was going to pick a thing that could plausibly break quantum mechanics, it would be black holes. How they satisfy unitarity is still an open question. If black holes aren't unitary... well, buckets of Nobel prizes and rethinking parts of QM is the result.)
