An interesting article The existence and abundance of`ghost' ancestors in biparental
populations By Simon Gravel and Mike Steel just appeared in the e-print collection arXiv.
It points out that there can be people who are the genealogical ancestor of at least one individual at the present but contribute nothing genetically to any individual at the present. These they call ghosts.
People who are the genealogical ancestor of all individuals at the present but contribute nothing genetically to any individual at the present they call super-ghosts.
Using a combination of simplified models, which I couldn't follow in detail, they show that approximately 0:5% of us will be super ghosts 100 generations from now.