Once you are baptized or confirmed as a Catholic, there's no way out. You are permanently marked as a Catholic, and you can only leave the Church by dying and going to hell. Even the souls in heaven and purgatory are part of the Church.
Excommunication is a "severe ecclesiastical penalty, which impedes the reception of the sacraments and the exercise of certain ecclesiastical acts" (CCC 1463). It is not expulsion from the Church, since indeed the Church cannot bind non-members, nor is it a declaration of spiritual condemnation.
Bishop Williamson and the other bishops of the Society of Saint Pius X (SSPX) were excommunicated for an audacious act of disobedience to the Pope's rightful authority in 1988. Earlier this year, that act was forgiven and the excommunication lifted. The bishops remain suspended, however, from the exercise of the functions of bishops and priests. Bishop Williamson is not allowed to act as a bishop.
One function of bishops is teaching. Bishops are to have a thorough and nuanced understanding of the Church and her teaching so they can instruct their flocks. So my jaw dropped when I read this quote attributed to the Archbishop of Freiburg, Germany, Robert Zollitsch:
"Mr. Williamson is impossible and irresponsible. I don't see a place for him anymore in the Catholic Church."
I can only assume that Archbishop Zollitsch is being quoted out of context by the German news magazine Der Spiegel. Perhaps he means there is no place for Williamson in the Church's heirarchy, that he should not have priestly or episcopal functions restored. But it is a fundamental tenet of the Catholic faith that there is a place for everyone in the Church. That's what the word "catholic" means: universal, applying to all people.
It's often said that the Church is not a museum for saints, but a hospital for sinners. World opinion is that Williamson is a grave sinner (although I leave that judgment to God).
That would mean he is a perfect candidate for membership in the Catholic Church.