What happened to Yui's Heart when Kirito wiped out his Inventory? Yui told Kirito that it would be a good idea for him to clear out his inventory as all the items were bugged and he could be detected by the system if they remained. As he was about to, he was hesitant in doing so. I can assume one of the 2 reasons:


All the items were a record of his 2 years in SAO and had a personal connection to them.
Yui's Heart was in the inventory and he was being careful not to delete it.


However, in the anime, it didn't show any sort of filter was applied and his entire inventory was cleared. So I am wondering what happened to Yui's Heart - was it not in his inventory because Yui was right beside him or was Yui protecting it in some way from the system so that it wouldn't appear in 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.