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Eucalyptus roots tend to be shallow compared to other trees, going down about 6-10 feet normally. They are very water hungry and if they cannot find a way to get enough water in the soil, may invade pipes. You can try giving it extra waterings, to keep it from seeking out water from the pipes or redirect runoff water to the tree for teh same effect.

This is damage that is consistent with cold damage. If the trees are still alive they should recover. Watch them carefully over the next few months while they recover as pests and disease are more likely to attack plants that are already stressed. As a preemptive measure, you can treat the trees with neem oil. This will help keep pests and fungus from attacking the plant.

This article will help you:
https://www.gardeningknowhow.com/ornamental/trees/eucalyptus/propagating-eucalyptus-plants.htm

They can die if it gets too cold, but you can check to see if they are alive and how far back they are still alive. This article will help with that:
https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm

There are several things that could cause this in your tree. If you have had colder than usual winters for the past two years, the stress from the cold may have hurt it. The tree may also have a pest or a fungus. I would recommend treating the remaining tree with neem oil. It will kill both pests and fungus on the tree. You may also want a local tree expert to come out and look at the tree to more accurately diagnosis the problem.

The unusually cold temps have done a number on many plants this year. Yes, it is possible that they may have died, but it is not for certain. Older trees can survive cold spells for short periods with only leaf loss as damage. This article will help you determine if the plant is still alive:
https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm