A black-hole is not a place that humans want to go. Travel into and past a black-hole’s event horizon and the danger posed by the black-hole’s gravitation increases to deadly proportions. This same danger of uninhabitable conditions is also found if you travel too close to a star, Or if you travel to most of the planets in our solar system, land on their surfaces (if they have any), and try to live there without wearing a spacesuit.
Similar to the uninhabitable planets in our solar system, not every exoplanet is inhabitable either. And yet the notion of space-time holds up around and on the surfaces of these planets. Some may object that this is all theoretical, and they aren’t wrong, this is theoretical physics.
Black-holes, although having their own special qualities, may not in certain aspects be too different in some of their qualities to large planets such as Jupiter or Saturn. The fact they have immense densities and gravity strong enough to trap light is indeed their uniquenesses.
It is important to remember that there are two separate notions of Space. One is the empty void of the universe. The other is the concept of Space-Time. Also, space-time is a relative thing, in more ways than one.
So consider a scenario where two space-ships are parked outside a Black-hole. One space-ship travels into the black-hole and the other does not. Suppose the first space-ship that travelled into the black-hole never returned but was destroyed by the gravitational forces or the black-hole. Space-time will have ended for that particular spaceship. And yet space-time for the spaceship parked outside the black-hole would be unaffected. The same would be true if you had two spaceships parked near an far-away exoplanet, or even parked in orbit around Jupiter or Saturn.