I don't even know what you said to tell you the truth.
An "Unbelieving Catholic" is a LOST SINNER.
An "Unbelieving Protestant" is a LOST SINNER!
How can an unbeliever be a Catholic??????
As Catholics, we believe that the Sacrament of Baptism leaves an indelible spiritual mark on a person. And this spiritual mark is tied to membership. Once baptised into the Church Catholic, you cannot change that fact that this event has occurred, and membership is simply a recognition of this fact.
If a defected Catholic wants to return to the Catholic Church, he will be treated as if he had been a member all along, i.e. no need to write to the bishop to be admitted into the Faith, no need for Baptism and Confirmation etc.
Of course, for tax purposes and other legal purposes, you can opt out of the Church. For example, here in Norway, you can only be a member of one religious group at a time, and all religious groups receive money from church taxes, proportional to their member count. So if a Catholic here registered as a member of, say, the Baptist Union of Norway, the Kingdom of Norway would for all legal purposes regard this person as a Baptist, and his name would be struck from the Norwegian Catholic membership register (the Catholic Church in Norway would still keep a copy of his certificate of Baptism and Confirmation, however), and his taxes would now go to the Baptist Union. I'm sure many other countries with a church tax system does things similarly. (Ok, Norway doesn't have a true church tax, only a sort of quasi-taxation, but that's irrelevant to my point here.)
The Catholic Church is, however, not only a physical political entity, but also a spiritual entity, as the Church of Christ subsists in the Catholic Church. Physically, you can opt out, but spiritually, you cannot, since you cannot remove the irremovable mark of Baptism. (Legend has it that the Roman emperor Julian the Apostate tried to wash away the mark of Baptism by bathing in pig's blood.) You might not believe that Baptism does these things, but the Catholic Church certainly does.
So if a Catholic commits heresy or is in the state of mortal sin, he is said to be severed from the Soul of the Church (i.e. lost), whilst still being in the Body of the Church (i.e. being Catholic), and is then under the obligation to repent and confess as soon as possible. I'm not familiar with the minutiae here, but I think that is the gist of it.
So how can an unbeliever still be Catholic? For one, he can be extremely bad at being Catholic. He might stopping self-identifying as a Catholic, and others might too, but the Church won't let go, and the offer of grace to come, repent and confess still stands as long as that person lives. He might be a lost sinner, but Mother Church never gives up on her children. Even anathemas and excommunications are ultimately tools for conversion, as they aim at making the person repent, for the sake of their soul.
So many will nominally bear the name of Catholic (and the name of Christian in general), but will still be lost. So this is not the same as Universalism.