Eucalyptus tree

My parents have expressed concern over the condition of a eucalyptus tree in their garden (photos attached). Can anyone tell me if the tree is dying or indeed dead? It leans at a very precarious angle and they're fearful that it may fall. Having said that it feels sturdy enough and I certainly don't want to cut down a viable tree. Thank you in anticipation. . . .

 

I wonder what caused the damage to the tree? It looks quite severe but a bit difficult to tell without actually seeing the tree. Your 1st photo is showing the tree has leaves so I don’t think it is dead completely, just from the photos about half the trunk looks in poor shape.
The biggest issue is Eucalyptus trees are very shallow rooted. Add in the health of the tree and I would unfortunately be inclined if not to fell certainly lop it considerably. Depending on the prevailing wind the tree looks like it could cause damage to fencing and maybe fall into the neighbour’s garden?
I have an enormous Eucalyptus without the damage your tree has and I often am a bit anxious if it is very windy but luckily apart from mess it would not cause any real damage if it falls down. Eucalyptus responds very well to being pruned severely which is perhaps what I would do. Ideally this should done in early spring. I am not sure if it is a bit late to do the pruning now. If not dire maybe leave it until next spring.

 

It looks a bit precarious to me and sadly I think I would get rid to be on the safe side.

 

I'm wondering if someone had a bonfire right next to it at some stage?

I think is alive but had it's day in that kind of location, It could possibly go on as it appears to be healing the wound.
Just not safe really.

 

Could probably pollard it just above the first fresh growth it won't look pretty but thinking again I'll stick with my first thought..sadly if it was mine it would have to go.