I agree with Sanskriti. I had no acceptances first try, directly out of undergrad. In my second try, I've gotten a few offers already, and waiting on the other universities before making my final decision. Is your family member applying directly out of undergrad? Taking a year off isn't going to hurt them.
I've always been told by professors not to take an unfunded position. While it is a debt thing, my professors were also of the opinion that the department didn't think highly enough of me to admit me if all they could offer was an unfunded position. While opinions may vary around the reasons why you don't take an unfunded position, its almost universal that you shouldn't accept an unfunded offer.