Q.If Mature 8’ X 8’ Silver Thorn In Full Sun Is Cut Back To 4’x4’, Will It Live?
Headgear after least 10 yrs old , trunk and branched at 4’ height are 1-2.5” thick. I doubt there will be any leaves left after cutting back to 4’x4’

Certified GKH Gardening Expert
It is considered invasive in some areas, so it has a will to live. It can be hard pruned if it gets out of control. It is best to shape it by removing selective branches rather than shortening all the branches.
https://plants.ces.ncsu.edu/plants/elaeagnus-pungens/
https://gardeningsolutions.ifas.ufl.edu/plants/trees-and-shrubs/shrubs/silverthorn.html