Generally speaking, statues that are worshipped are considered avodah zarah – forbidden idol worship – and it is forbidden to derive benefit from them. Nevertheless the Gemara on today’s daf (=page) teaches that if a statue falls apart and breaks into pieces, it may be permitted. Resh Lakish argues that it becomes permitted since it is clear that a broken idol has no power. If it could not protect itself, who could possibly believe that it has the ability to protect others?! Rabbi Yohanan disagrees. According to Rabbi Yohanan, an idol is only voided if it is negated by a non-Jew, and that does not happen in this case.
The halakhah allows a non-Jew who chooses to negate his idol the right to do so. The question is whether a statue that is found broken into pieces, is a “still worshipped” idol. Some point to a passage in the Talmud Yerushalmi that explains that if the idol is broken such that it will likely be put back together, all would agree that it remains forbidden. Similarly, if the idol is broken such that it is clear that it will not be put back together, then all would agree that it becomes permitted. The difference of opinion is only in a case where the future use of the broken idol remains unclear.
The Hazon Ish suggests that according to Resh Lakish making use of the broken idol is permitted even if its owner is unaware that the idol had broken. Since this idol can no longer be worshipped in its current condition, its status as avodah zara disappears on its own. Furthermore, even if the idol can be repaired, given its present status it is considered to be insignificant and is not considered to be avodah zara. Rabbi Yohanan who disagrees would argue that it is still honored by its worshipers in recognition of its past glory, and that honor keeps it from being considered null and void.