Currently the Catholic Church has a Pope Emeritus (Benedict XVI). This is, to the best of my knowledge, the first time that such position has existed. There have been and still are plenty of bishop emeritus elsewhere, but this is the first time it happens in the diocese of Rome. Is he infallible?
This is more of an hypothetical question, as it seems unlikely Benedict XVI will ever attempt to speak about moral or faith issues ex cathedra. So far, he has rather kept a very low public profile. If he ever tries to, it will probably be with the consent (and perhaps sponsorship, if not directly under the name) of the Pope.
My guess is that he is not. In my view, the Chair of St. Peter is occupied by Pope Francis and not by Benedict XVI, so he has lost the infallible protection the Holy Spirit gives to the occupier of that Chair. But maybe I'm wrong. Any ideas?