The taurobolium is a kind of substitutionary sacrifice–a bull is sacrificed in place of the archigallus self-castrating in the Roman context, it appears, from the second century onwards. Other sacrifices involving Cybele will be dealt with here, however: the case of Demophoön and Phyllis, the former being the son of Theseus of Athens, and the latter being the princess of Thrace. (I have written about other important figures called Demophoön twice recently; the issue of whether there is a relationship between these ones will have to be left for another time, and may in fact be entirely irrelevant!) Perhaps there is some character of sacrifice involved in the tragic death of one or both of these figures, and both are connected to Magna Mater in some fashion.
The epitome of Pseudo-Apollodorus' Bibliotheke 6.16-17 gives their story as follows: