In war, when a victor shows no clemency or mercy and refuses to spare the life of a vanquished opponent in return for their unconditional surrender, he is said to “give no quarter” (or take no prisoners). Effectively, it’s a death sentence.
Before the 1300s, “quarter” meant the fourth part of something or the points of the compass. Eventually, the meaning expanded to an area of a city, particularly one occupied by a specific group, for example, “the Chinese quarter.” The same meaning was applied to a section of an army camp.
By the beginning of the 1300s, “quarter” began to be used to describe a region or local area. By 1591 CE, “quarters” became the common military term for a residence. A few short years later, written records used “quarters” as a verb meaning “to provide lodging for soldiers.” Not until 1611 CE was the phrase “to give no quarter” first recorded.
To house and feed a prisoner meant giving them quarters, so to refuse to quarter men who surrendered meant they would be put to death. Sometimes a red flag was raised to signal the intent to give no quarter. No reason is given for the color, but perhaps it was used because red is the color of blood. With the Hague Convention of 1907, it became illegal to grant no quarter. Eventually, “give no quarter” took on a figurative meaning of showing no mercy, usually applied in negotiation situations.
There were other applications. The idiom “to keep good quarters with” meant to have good relations with a person or persons, probably referring to the need to stay on good terms with those living with or near you. Shakespeare used it in The Comedy of Errors in 1590.
These days, the only time that I use “give no quarter” to mean a death sentence is when I have to deal with invading mice. My cat backs me up on this stance.