You'd kinda have to exclude any Doran, jungling, or basic starting item, buuuuut...
...I'm thinking in my head if that could reasonably apply to both teams, instead of people fighting each other for items. Supports might have it rough if they're both going for Frost Queen's Claim, and with one freaking Sightstone to go around.
You know, you helped me remember something, way back in the original Defense of the Ancients map for WarCraft 3. There was this item, I can't remember at all what it was called, but it dropped on death. It had stupid-high damage, but if you got killed with it, someone else could pick it up. The thing was exceptionally expensive, too.
So, following that, while I'm not saying you'd drop the item (coding would make that...kinda difficult, if you had six items to drop like some Diablo 2 boss), maybe you'd lose items on death, with the ability to re-buy them, but also give the other team an opportunity to do the same? Could make for some interesting strategies. You'd intentionally save up about twice as much gold as you needed to in case you died so you could re-buy any key mega-item, and it'd be a risk to buy one without that gold. But then the other team wouldn't have the item if it was purchased first by you, and they'd have to get to you before they could buy it themselves if they were risking that, unless you had enough gold already to re-buy it, and you'd have first access to the shop, anyway.
I dunno, just thinking out loud, but I admit I kinda like playing with the idea.
or 
before anyone else :D.
