I work in the foster care system and I've seen it happen a few times. Abuse and neglect by mom, usually a combo of mental health issues and addiction. If Dad shows up in court and says and does the right them, he is treated like royalty by the court. Everyone is amazed that a father has shown up. Most other times the father is completely out of the picture so the children go to a female relative or foster family.

I think the term "full custody" is thrown around very loosely and in an undefined manner.

Do you mean full physical custody? Full legal custody? No visitation rights whatosever?

I know of several situations where the dad has physical custody of the kids yes, but the mom has liberal visitations rights and has legal custodial rights over the children as well.

If you are talking about a situation where a court has stripped a mother of all legal, custodial, and visitation rights, that is extremely rare. It would be extremely rare for any parent.

DH has full custody - exwie didn't want the kids and gave them up willingly. No drugs or mental illness, just weird decision making process. (5 years later after DH and I got married, ex sued for custody of one of the kids. That was fun. Not.)