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How's this?

A neighbor had this going on starting a few years ago. I thought the tree was goner and entering the decrepit, old age phase. Surprisingly, it seems to be recovering over a 3-year period and doesn't look so bad today. I have no idea what the cause it.

But you can always remove dead foliage/branches. No need to wait.

Okay I have chopped out all the branches that were showing the symptoms. It was quite a pruning and the damage was a lot more than I could see just from the outside.The branches in total were usually shot, anything coming one of a main branch was dead.

So now I just wait?

Exactly, Wait, watch and see if it improves. If it doesn't show marked signs of improvement during this season, I'd chuck it.

They look like Ligustrum japonicum.

Should they ever be fertilized or anything like that?