Green’s Dictionary of Slang

1. (US Und.) a sentence of 15–30 days.

1904		‘Number 1500’ Life In Sing Sing 267: He calls out his remaining time [...] or forms the words with voiceless mouth so that they may be read on his lips, ‘two and a whop,’ or ‘one and a whisper,’ as the case may be.
1932		L.E. Lawes Twenty Thousand Years in Sing Sing 241: The judge gives a guy a sentence. When he arrives it becomes a ‘bit.’ Eventually it becomes a ‘stretch.’ Finally, on its last legs, it becomes a ‘whisper.’.

2. (US prison) the final portion of a sentence.

1931–4

D. Clemmer Prison Community (1940) 336/2: whisper, n. A term denoting the last few months of a prisoner’s sentence.