Answer: Eucalyptus are constantly shedding leaves, which turn red before they drop. It doesn't sound good when all the leaves drop at one time, but it doesn't necessarily mean the tree is completely dead. I'd wait to see if it produces new leaves in the next few weeks. If not, I would suspect a root problem - overly wet or poorly draining soils can suffocate tree roots; not enough water can kill trees, as well.
Eucalyptus are relatively disease free so I don't think you have anything to worry about in terms of a disease spreading to your second tree. Hope your tree produces new leaves!
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