So as you can see in the title, I just lost a legendary secondary engram. I just got it from a Roc strike playlist, and I went to the Tower cryptarch to redeem it, then exactly when I clicked the engram I started lagging and it said "Contacting Destiny Servers" over and over until I disconnected. I was a little bit annoyed by it, but then when I got back into the game I was excited to redeem my engram... When I opened my inventory menu I saw that the engram was gone, and I had no new secondary weapons either, and I hadn't gotten any more materials. It just went poof.
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Unfortunately, Bungie does not replace lost or dismantled gear for any reason. https://www.bungie.net/en/Help/Article/12211