Weekly heroic matchmaking dropped me into a strike after Phogoth was already dead. The countdown was already going when I spawned. My warlock got a set of hunter boots out of that.

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I had that happen in Crota last week. I noticed a group on my friends list with less than 6 people, joined the fireteam, and got Hunger of Crota while my ship was coming down from orbit. I stuck around for the next few games out of gratitude - whatever they did, I helped. :)

Nice, I spawned in with the ole' ogre at about 10% health and the two other guys in there crouching in the entrance room. It was over in about 30 seconds and I was 9 coins richer :D

Same thing happened to me with a LFG Crota run. I was looking for a fresh run and they posted as a fresh run. I join the fireteam and they are at crota. They revived me for the final round on Crota and I got the Light of the Abyss and Another Helmet. I felt bad about that lol.