Could planets survive their star becoming a black hole? Would the supernova responsible for its formation destroy them. The question becomes one of how destructive the supernova event is to its own solar system - does it completely evaporate all planets up to and including Jupiter size?
The duplicate deals with "safe distance". I want to know whether any planets in a solar system like ours would survive. In other words, would something like Jupiter be completely evaporated or blown out of orbit
 A: When black holes form from the collapse of stars, we think they usually produce bright supernovae explosions which release tremendous amounts of energy.  Some models suggest that a non-negligible fraction of stars which produce black holes may not produce normal supernovae, these are often called 'failed supernovae', see for example astrobites: Gone Without A Bang.  In this case, a 'weak' explosion is still, likely, produced --- but may be too weak to destroy/damage surrounding planets.
More typical supernovae will remove all the atmosphere from rocky planets, and some fraction of the atmosphere from gas giants (see also: this article, some minor issues though).  But, likely, most planets in the habitable zone wouldn't actually be destroyed.  So the planets could survive, but life on them likely would not.
One additional consideration is that the remnants of supernovae (neutron stars and black holes) are known to receive 'kicks' from the explosion.  Asymmetries in the blast can cause the remnant to recoil at large velocities (up to 100s of km/s).  These are believed to be somewhat lower for black holes, but still, depending on the magnitude of the kick --- planets could definitely be lost.  This is one way of creating 'rogue' or 'runaway' planets.
A: A black hole $m\approx300,000M_{sun}$ at the center of galaxy $NGC 4845$ is thought to have a giant gas planet with the mass no larger than that of a brown star in orbit, though it is currently being drained into the black hole. (And by currently I mean what we are seeing right now, which happened a long time ago).
The gas giant is thought to have been ejected from a star system.
Rocky inner planets will probably have been swallowed up by any star at the end of its life cycle. The preservation of any planets around a star that goes supernova is highly unlikely.
So.... kinda?
