Alive and dead at the edge of a black hole?

The event horizon of a black hole is what is called a "coordinate singularity", which is a point in space-time that appears to be a singularity in some coordinate systems, but isn't a true singularity. In the coordinate system of a stationary observer, all the points of the event horizon are at "infinite" time, so things moving towards the event horizon will appear never to reach it. But in the coordinate system of an observer actually falling towards the black hole, the event horizon is no different from any other point in space-time.