165. How an Idol is Nullified
Avodas Kochavim 8:10
An idol is nullified when a non-Jewish idolator cuts off the tip of its nose, ear, or finger, or rubs its face smooth even though no part of it is destroyed. He can also nullify the idol by selling it to a Jewish craftsman. However, if the non-Jewish idolator used the idol as collateral for a loan, sold it to another non-Jew or to a Jew who is not a craftsman, or if he abandoned it after it was covered by fallen debris, or did not demand it back after it was stolen, or if he spat on it, urinated on it, dragged it on the ground, or threw excrement at it - in any of these cases, the idol is not nullified.
Avodas Kochavim 8:11
If an idol is abandoned by its worshippers in a time of peace, it is clear that they have nullified it and one may derive benefit from it. If the idol is abandoned in a time of war, it remains prohibited. The assumption in such a case is not that the idol was nullified but that its adherents fled because of the war.
If an idol happens to break on its own, it is not permitted to derive benefit from the pieces until they are nullified. Therefore, if one finds broken pieces of an idol, they must be presumed to be un-nullified and prohibited. If the average person could reassemble the pieces of the idol, then each piece must be nullified separately. If the average person could not reassemble the idol, then once one piece has been nullified, the rest of them are also nullified.