Q.Why Are Green Burford Holly Berries Turning Brown And Shriveling Up?
Tons of green berries on plant are turning brown.

Certified GKH Gardening Expert
This is likely one of several root rots that can plague this plant.
Phytopthora is suspect, but there are several. Identification will require microscopy and staining, which can be done at your closest extension service. Probably, this is will be UT Chattanooga. Here is an article that will help you to find your closes extension service:
https://www.gardeningknowhow.com/extension-search
This article will help you with fungicide use:
https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm
This collection of articles will help you to grow Holly shrubs: