Quote Originally Posted by Kuero View Post
Mine also dropped from a box, I'm still remembering really good on it because I almost made the wrong decision. It was the last destructible item in morhaven rooftops run and I was so far away already that I first was too lazy to run back for and destroy it, then after killing the boss I couldn't resist my perfectionism anymore and went back for the box. It was a smart move because the bats dropped from that box

I don't think drops are predetermined when you join a game, I believe its a code roll every time you kill or destroy something.
So any box or enemy you leave behind is not potentially holding your good drop, rather they just are another lottery ticket.