Both Uses of

cleave
in
One Flew Over the Cuckoo's Nest

I sat up in bed, and my shadow fell across the body, seeming to cleave it in half between the hips and the shoulders, leaving only a black space.
Chpt 29 *

cleave = split

I'm mopping near the ward door when a key hits it from the other side and I know it's the Big Nurse by the way the lockworks cleave to the key, soft and swift and familiar she been around locks so long.†
Chpt 1

Definitions:

(1) (cleave as in: cleave through)
to split or cut through something

Ironically, this word can mean to split in two or to hold together.

Note that you may see cleaved, cleft, clove, or cloven as the past tense of this sense of cleave.
(2) (cleave as in: cleave to)
to hold firmly to something -- such as an object, a person or idea

Ironically, this word can mean to split in two or to hold together.

Note that you may see cleaved, clove, or clave as the past tense of this sense of cleave.
(3) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

a proper noun or other word too rare to warrant focus