I have two euonymus bushes in front of my house that are about twenty years old. They have always done well and survived many cold winters. But this year they have started dying from the center outward. The stems and leaves have turned black and the bushes have lost their leaves. I have never seen them shed their leaves before.
It's likely that this is winter injury. This plant is hardy to Zone 7, and can be severely damaged by low winter temperatures.The sudden temperature swings high and low may have also been a factor. Plus, we had a droughty fall and winter, and broad-leaved evergreens usually suffer winter damage when their roots don't have enough moisture in winter.
Prune out the dead wood. If it puts out new growth, the roots survived. If it is too misshappened, you will probably want to replace them. Otherwise, you may want to give them a year to recover and then prune into a better shape.