I think it'll just save to wherever your character was last...
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But like I said what if you join another raid party and they're behind you or ahead of you?
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Then yes, I assume that you won't be left at the door. You'll probably spawn in with the party leader as long as he's not super far ahead or super far behind. But giving everything that Bungie has told us, I assume that team work will be needed. I doubt you'll be too far away from your party members at any given time. So yeah, you'll just spawn in wherever the majority of them are. And probably lose progress of any other raids you had going on.