How big are these pieces of "DEBRIS"? Just trying to eliminate insect or animal droppings as a possibility.

Does your sink have black soundproofing on the underside?

They are hard like small stones/shavings. They are not animal droppings.

No. The debris is stone hard, half inch pieces and some dust.

What is your sink made of? How old is it? Have you shined a flashlight up in there? Do you have a garbage disposer? Is any of the dust rust?

But I'm still wondering about the stuff on the underside of old cast iron sinks, which was black and did tend to flake.

The sink and house is 16 years old. I do have a disposal. The underside of this stainless steel sink is white. I shined a flash light and can't see where it is coming from. Yes, some of the pieces have a little rust, but mostly black.

Bug Poo can be rock hard... but it can be as was suggested Petrified sound deadener, though I'm surprised why the chunks are so small if it's that.