Bungie, please allow for players who lose connection to your servers to rejoin all missions but most importantly GMs. To do all the work to get to the last phase of a GM and get a dropped connection isn't just a pain for me but for the other two random players that joined up. It's such a pain in the rear and has nothing to do with preventing character or equipment swapping.
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If you want this, it is only fair that there be no extra rewards from killing any champions from the GM, but rewards for completing the Nightfall stay the same. Also it would have to be the same character that started the GM, which is easily traceable (think trials rejoin)