In the rare case where enough -1/-1 counters are placed on Idol of False Gods to reduce its toughness to 0 or less while it's a creature because of the effect of its last ability, Idol of False Gods will be put into its owner's graveyard when state-based actions are performed. Effects that care about the number and types of counters that were on Idol of False Gods when it died will see both the +1/+1 and -1/-1 counters, and any effects that trigger "whenever a modified creature dies" will still trigger.