Arkham Horror
Is an item, ally or talent discarded once its damage or horror reaches its health or sanity?
The rulebook's Assigning Damage and Horror section says an asset with damage or horror at its stat must be discarded.
Yes. Reaching or exceeding either stat, health or sanity, discards the asset, and one harm step can reach both. Talents are discarded the same way, though they cannot be traded. Damage and horror from one source apply at the same time, so all of it can go on the card before it is discarded.