I know of no graveyards for broken holy items. But a blessed crucifix or a blessed statue is not just an ordinary item: it is blessed. And blessed objects should be treated with reverence.
If you cannot fix the item, or you have no use for it, you may discard the item by incineration, burial or pious disposal.
There are no hard-and-fast rules for “pious disposal,” but common sense should help you figure it out. What you want to avoid is someone combing through the garbage only to discover a statue of the Blessed Mother in the dumpster. That’s no way to treat a lady, and certainly no way to treat Our Lady.
Rev. Francis Hoffman, J.C.D., Executive Director of Relevant Radio. Follow him on his Facebook page “Father Rocky.”