Jason P. answered 11/28/20
Completing my M.A. in Applied Linguistics
This of course depends on where in the world you are talking about and what exactly you wualify as "Late Byzantine," because many other languages were being used in written in that time, and the Byzantines went of for a while. Arabic writing was increasingly becoming more popular throughout Arabia, and the script was being adapted to surrounding languages. Farther East, China, Korea, and Japan were also putting their writing systems to good work for both history and literature. Those are just a few quick examples from around the world, but even in Europe the Latin script was being used to write European languages in the early Middle Ages.