Like the title says. If a creature with the petrified condition is dropped to 0 HP, what happens? Does the petrified effect end, and they're globs of meat? Does the soul leave the statue at that point, or is it still trapped inside?
The creature would make normal death saving throws at 0 hit points. Their corpse would remain inanimate material after being killed. The stone form persists until properly cured as per the petrification description in the monster's ability or the spell wears off on its own (e.g. flesh to stone).
The Petrified condition states:
A petrified creature is transformed, along with any nonmagical object it is wearing or carrying, into a solid inanimate substance (usually stone). Its weight increases by a factor of ten, and it ceases aging.
The creature is incapacitated (see the condition), can’t move or speak, and is unaware of its surroundings.
Attack rolls against the creature have advantage.
The creature automatically fails Strength and Dexterity saving throws.
The creature has resistance to all damage.
The creature is immune to poison and disease, although a poison or disease already in its system is suspended, not neutralized.
At 0 hit points, they would begin making death saves as normal. The petrified condition does not modify the death and dying mechanics.