Is the original paint hard to get off? Could it possibly be milk paint, the old kind. They say that is almost impossible to remove. Also, the color sounds like it could be milk paint. Depending how old the piece is could determine if it is truly colored with blood.

My father, years ago, tried to refinish an old hutch that was painted with reddish milk paint. He never could get the red cast out of the wood. Later he found out that it would have been worth a lot more if he hadn't refinished it.