Bronze statues were melted down, and the bronze reused for weapons or other artifacts. As Jack Rich indicates in The Materials and Methods of Sculpture, Greek bronzes, "were seized and quickly melted down by the Roman, Turkish, Venetian, and other invaders." Romans collected Greek art, commissioning marble copies. Marble is not nearly as reusable as bronze, especially when it has been carved into a sculpture (the marble used to construct buildings in Roman antiquity, in contrast, was reused for other buildings). In addition, collecting marble sculptures became fashionable in the Renaissance, which further ensure that the marble copies would subsist.

Regarding bronze statuary in Greece see this brief article from the MET website.