Answer:
Archaic language
Explanation:
In this question, the phrase "let them have their sleep out" is an example of archaic language. Archaic language refers to the use of words that can be considered too old to be understood by the general population in most contexts. These words are not in current usage anymore, or are now used with a different meaning. Archaic language is usually encountered in older examples of literature, and not those written in recent times.