This is a strong evidence that stats are generated when item drops.
Now, if the stats are not stored in the client, where does it get stored? Server, obviously. In other words, does server hold the stat / states of all items?
It is plausible. Maybe each item has a GUID.
Yes, each item has a unique ID that is stored server side. That's how all items are checked against ith/dupe scanner upon joining a game. Same reason as to why you can have 2 sojs, but they don't clash with each other and make one of them delete from the dupe scanner when you join the game... Because each of them has a unique item ID. But, if you were to dupe one of those sojs, keep them both on the same character, then one of them would poof upon leaving and joining a game.
When you leave a game all items on your character are scanned against all other items on the same server IP and if two items (or more) have the same item ID, the people still remaining in the games on that server will have their items flagged for deletion. But, of course you can temp perm and bypass this, but without that, the items would be flagged for deletion.
Long story short; yes items have unique item IDs that are stored server side and they're used for dupe checks more than anything, but the item ID and all info about the item is assigned to it the moment it is dropped from monster/chest/clickable.