What unusual does a worm-like creature Lithoredo abatanica (pictured) feed on?

well... guess you learn something new every day! 👍

It may burrow into stones, but it does not "feed" on them, as stones do not contain the organic matter that all heterotrophs need.

I live near this place but I have not seen this...

I think litho/lithos is Greek for stone? so lithoredo was a clue