I haven’t heard of tar paper being used as underlayment, but I have used big rolls of paper for that. In my understanding, the point for the paper is to allow the wood to be able to move seasonally, and to prevent squeaking.
I don’t think I’d want to use tar paper, though, cause it’s hydrophobic. Whatever finish is going on the wood is going to also be a water barrier, and it’s a general rule of thumb to never have 2 water barriers next to each other in a house. That’s how you get trapped water that can damage stuff. If you spill water, and it makes it in a little gap between floorboards, it could just sit there indefinitely.
I could be wrong, though.
I just read into it a little bit. Seems that I was wrong, and “tar paper” is typically not completely waterproof, it’s just water resistant. Most stuff these days isn’t technically tar paper, either, it’s roofing felt. I guess it’s only called paper if it’s made from cellulose. Apparently they did make the felt from asbestos back in the day.
Seems like it’s definitely common enough to use it under flooring, especially if it’s a thinner grade.