I just posted this question about whether you continue making death saving throws while petrified if you are at 0 HP. The answer was yes. But I thought of another question:
If you are downed and petrified, you must still make death saving throws. Can you receive healing or Medicine checks in order to stabilize you (so you stop making death saving throws) while in this condition?
In addition, if you survive, are you able to recover hit points either by healing magic (from other PC), potions, taking a long rest, or spending hit dice on a short rest? I mean, are you able to recover hit points by any source of healing while petrified?