A crucifix is two objects assembled as one, the cross itself and the corpus, the figure of Christ fixed to it, and each is usually made separately before being joined.
Corpus and cross as separate crafts
A wooden crucifix typically has a carved corpus, often boxwood or lime, pinned or glued to a cross of the same or a plainer wood. Cast examples use bronze, brass or silver for the corpus, sometimes gilt, fixed with nails through the hands and feet in imitation of the execution itself. Baroque workshops in Spain and its former colonies carried this furthest, producing polychrome corpora with glass eyes, real hair and jointed arms for use in Holy Week processions, figures meant to be dressed and carried, a tradition still active today.
Ownership, blessing and what is not for sale
Any Catholic may own and use a small crucifix without ceremony, but a large altar or processional crucifix belongs to the parish, is blessed for that specific use, and is handled during the liturgy only by clergy and servers. A damaged crucifix follows the same disposal custom as a plain cross, burial or burning rather than the rubbish bin, though where corpus and cross can be separated, a badly damaged figure is sometimes replaced on an otherwise sound cross rather than discarding the whole. Processional figures of unusual age or artistic value are treated as parish patrimony and cannot simply be sold, a rule that has stopped more than one attempted sale of a colonial era Christ figure out of a struggling parish.