What happened to Yui's Heart when Kirito wiped out his Inventory?
Like your previous question, I don't think there's a way to confirm exactly what happened here, but I have 3 possible explanations.


Yui's Heart was marked as a special item and couldn't be deleted (e.g. Quest item, etc.), but I think this is the least likely, since as you said, the anime showed his inventory being empty and there was no filter on it.
It could simply just have been consumed when Yui was summoned, so it was already gone when he deleted everything.
It was simply deleted. Since Yui was already initialized in the world, it didn't matter if he had it in his inventory or not.