About "involuntary Catholics"
While that distinction isn't recognized by the Church, it's an understandable condition to consider. It all starts with baptism, as with the previous answer that you linked to.
Baptism provides a permanent mark on the soul
Semel catholicus, semper catholicus (per Canon Law)
(Canon 11) The law recognizes as Catholic anyone baptized in the Catholic Church or received into it1.
If you are baptized Catholic, but naught else is done to raise you in the faith, the Church will still consider you Catholic (per Canon 111, among other considerations). This is directly related to the indelible spiritual mark on your soul that occurs during the baptism.
CCC 1272 Incorporated into Christ by Baptism, the person baptized is
configured to Christ. Baptism seals the Christian with the indelible
spiritual mark (character) of his belonging to Christ. No sin can
erase this mark, even if sin prevents Baptism from bearing the fruits
of salvation. 83 Given once for all, Baptism cannot be repeated.
It is important to recall that the Catholic Faith is not a single event; the intent of being brought into the Catholic Faith Community (at whatever age) is to live our lives in the Catholic faith community (the church is the body of Christ) and to (as best we can) configure our lives to Christ.
Would they be considered Catholic, up to such point that the person intentionally renounced this?
Yes (and even if they renounce their baptized faith ;-) ) .
The Church will not renounce its connection to that person, though a person may leave the faith community by word, deed, or both.
1279 The fruit of Baptism, or baptismal grace, is a rich reality that
includes forgiveness of original sin and all personal sins, birth into
the new life by which man becomes an adoptive son of the Father, a
member of Christ and a temple of the Holy Spirit. By this very fact
the person baptized is incorporated into the Church, the Body of
Christ, and made a sharer in the priesthood of Christ.
Your question appears to be referring to a Lapsed Catholic
Lapsed Catholics are all over the place. In the past few years I have (as part of the RCIA ministry) been of assistance to help some lapsed Catholics return to the Faith, to get confirmed, and to convalidate their marriages. (I am not a clergyman of any sort; lay person, volunteer, catechist).
A lapsed Catholic is a baptized Catholic who is non-practicing. Such a person may still identify as a Catholic and remains a Catholic according to canon law.
The canon law support to the answer may seen a little indirect, but it provides a clear idea on how the Church sees the relationship between the Baptized and the Church.
Can. 11 Merely ecclesiastical laws bind those who have been baptized
in the Catholic Church or received into it, possess the efficient use
of reason, and, unless the law expressly provides otherwise, have
completed seven years of age. {standard age of reason}
While there are a variety of reasons that people profess to leave or ignore the faith they were baptized into, the Church has an outreach program called Catholic Come Home. A core message is:
Regardless of why you left or got out of the habit of going to Mass,
you can always come home and return to the practice of the sacraments
and the fullness of relationship with Jesus Christ and the Church he
founded. We are Catholic. Welcome home.
1 New Commentary on the Code of Canon Law, ed. by John P. Beal, James A. Coriden, Thomas J. Green, Paulist Press, 2000, p. 63 (commentary on canon 11
Even the form of censure known as excommunication does not in itself make a person an ex-Catholic: excommunicated persons are "cut off from
the Church", barred from receiving the Eucharist and from taking an active part in the liturgy (reading, serving at the altar, etc.), but they remain Catholics.[11] They are urged to retain a relationship with the Church, as the goal is to encourage them to repent {via the sacrament of penance and reconciliation} and return to active participation in its life.