Event horizon for observer within main horizon

[Swamp Thing]

TL;DR

If an observer is within the event horizon of a black hole, is there another horizon further in such that light/causality can't reach that observer?

The event horizon of a black hole is defined with respect to observers far away, and we know that light from within the horizon can't reach a distant observer.

But what if an observer is within the "main" event horizon? Presumably, there will be another horizon nearer to the center, such that light from within this horizon can't reach this observer? If so, is there a technical term for a "subjective" horizon defined wrt an observer located at a distance x inwards from the "real" or "absolute" horizon?

 

[Ibix]

An event horizon isn't defined with respect to any observer. It's the boundary between regions that can send light signals to future null infinity and those that cannot. As such, it's an invariant property of spacetime, and your question has an invalid premise.

There are certainly regions of the black hole interior that cannot send signals to a given observer. If that observer crashes into the singularity, any light that didn't reach them before that never will. The boundary is just the past light cone of the impact event. This is not an event horizon, though, since it's an observer dependent boundary and not a property of the spacetime.

Also, black holes don't have centers, so speaking of "closer to the center" doesn't make sense. Their interior volume is infinite, and the singularity isn't a place, but rather more like a time (one in your future if you cross the event horizon).