Question
I am a local "handy man"  and have had multiple calls concerning Globe Willows that appeared healthy then started weeping sap and small wood chips.  I am aware of some of the bores that can cause this condition. Although not all these trees have shown the discharge of wood. My neighbor trimmed the tree back to the main branches where the wood appeared healthy. These limbs had a black center and were slowly dropping the dead leaves. What do you recommend we do with these trees?

Answer
If the tree still has green foliage I would try treating the trees with an insecticide called Bayer Advanced Tree and Shrub Insect Control. This is applied to the soil around the tree and the roots carry the insecticide to the trunk and branches and when a borer enters the tree it is killed. This will prevent borer attack for the season. Here is a web link to this product--check with your local garden type store for it.

IF there is little green left on the tree you might as well remove it. But if there is green I would try to save what you can.  

http://www.bayeradvanced.com/tree-shrub-care/products/12-month-tree-shrub-insect