Green’s Dictionary of Slang

cop out v.2

[cop a plea v.]

1. [1930s+] (US Und., also cop out on) to confess, to inform.

2. [1930s+] (US Und.) to use legal plea-bargaining to plead guilty to a lesser charge in return for having one dropped.

3. [1940s+] to avoid a problem or a difficult situation, to run away, to give up trying.

4. [1950s] (US black/jazz) to go to sleep.

5. [1960s+] (also cop out on) to let down, to betray.

In phrases

cop (out) to (v.)

[1940s+] (US) to admit, to confess, to take responsibility for.