So what would it be to make a black hole "the most dangerous body" in the game?
If a black hole is dormant and no matter is falling into it it doesn't emitt a lot of radiation. It's gravity is strong, true, but only very close to it. It's not a vacuum cleaner sucking in everything over great distances. FSD technology should clearly be capable of compensating a BH's gravity well outside its event horizon.
On the other hand a black hole influences spacetime in that it starts to bend it according to its mass and gravity. If a frame shift drive truly folds spacetime without the ship getting fryed by incoming blueshifted electromagnetic radiation, a black hole may severly hamper an FSD's performance and maybe pull the ship in as folded spacetime would approach the event horizon and the speculative singularity inside the hole.
Current game mechanics make your ship's heat rise slowly when approaching a BH and then you are dumped out of supercruise. You could argue, the FSD reached its maximum rate of folding spacetime and that it's an emergency exit. Once below SC speeds however, the BH's gravity would start to affect the ship, maybe pretty much like the jets of a neutron star does. But in this case the "jet effect" would be more like an invisible sphere around the hole. When you hit the zone, you have to struggle getting back to SC or your ship gets torn apart due to gravitational strains.
The thing is, the debris and the pilot would be drawn into the singularity of the black hole and thus would be removed from the physics of our universe. So yes, in all consequence, your save would be deleted. If one was to implement this as a consequence...
It's an interesting thing to think of, no doubt...