Not necessarily. The estate would happily sue and prove that the descendants would suffer if certain unsavory details would come out, so they must never do. Just like copyrights and such are extended way past the life of the creator, so can be other privileges. As soon as we accept the premise that you own and can control what others think and tell about you, it does not have to stop with your death, just as any other things you own do not become unowned after you die - they just become part of your estate and then can be owned by whoever inherits it.
