Are you looking for hard evidence? "Proof"? You are not going to find it. You can only "suppose" from family stories, which are generally more true than not. Even finding ancestors' births recorded in the slaveholder's Bible is no "proof" that the slave named is a family member, but it certainly looks that it "might" be. That some slaveholders freed their offspring serves as a "feel good" thought, but it was certainly rare. This last explanation serves to assuage pain and guilt and is often (but not always) offered up by the descendants of the slaveholders.