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The entire assembly is held on by phillip head screws. Two on the door and two on the unit, but the latch is attached with a pin of some sort. Is this the part that came undone?
I've seen photos of extra latches that people added. They looked to be the same type as the original latch. You should be able to pick one up at the local home improvement store and replace the broken one.
Yes, that's exactly what came undone. Thanks for getting my brief explanation! Wasn't quite sure I explained it good enough. I'll have to look and see what I can replace it with. Thanks!