What aspect of it are you referring to in particular? Chain cases were very common on English roadster bicycles from the late-19th century all the way up until the 1960s and were thereafter limited to rather "old fashioned" models. The current model of Pashley Sovereign still features a full chain case. The way this one works is a Sunbeam innovation that allows the rear wheel to be removed for changing the tire without having to completely disassemble the chain case, which is a really useful feature.

In the particular case of the Sunbeam, the cases were also made to be liquid-tight and filled with enough oil to constantly lubricate the chain during use, and this was known as the "oil bath" chain case. I think this particular model is a bit later than the heyday for that innovation because it was made after Sunbeam expanded their operations band the quality of their work went downhill to some extent after the company changed hands.

-Gregory