Here is an explanation of why they are called deathlayers:
"There are two competing theories. A literal translation of its German name, Totleger, means “death layer.” One theory has it that the name was bestowed because the hens of this breed are so productive they lay an egg each day until the day they die. The second theory – less sensational but probably more accurate -- is that the breed was first described by a different name in low German (Dauerleger or, literally, “day layer”), and over the centuries this name morphed into Totleger. Either way, what cannot be denied is that the Deathlayers do lay a large volume of medium-sized white eggs"
source:
https://greenfirefarms.com/deathlayer.html
(Greenfire farms imported some to the US from Germany, and has been selling them since then.)