Green’s Dictionary of Slang

1. a county workhouse or local prison.

1675		Head Art of Wheedling 311: Now and then some Cracking Sempstress, or Free Trader [...] have the ill hap to be Confined within this stony Band box.
1931		G. Milburn ‘Convicts’ Jargon’ in AS VI:6 437: band-box, n. A county workhouse or penitentiary.
1936		Mencken Amer. Lang. (4th edn) 580: In virtually all American prisons [...] a county workhouse is a band-box, and a police-station is a can.
1949		Monteleone Criminal Sl. (rev. edn).
1951		D. Dressler Parole Chief 262: If they stop you they know right away you’re a recruit for the bandbox.
1992		Bentley & Corbett Prison Sl. 3: Band Box A county workhouse or prison.

2. (US black) a sitting-room.

1941

D. Burley N.Y. Amsterdam Star-News 17 May 11: [P]ast the smoker, past the nodpad, past the dive-pond and into the bandbox.

3. (Aus.) the posterior, the buttocks.

1933

Bulletin (Sydney) 6 Sept. 41/2: Yargus butted The Snake in the pantry. The Snake dug his knee into Yargus’s band-box.

4. a prison from which it is easy to escape.

1950

Goldin et al. DAUL 22/2: Bandbox. 1. Any prison or jail from which it is easy to escape.