Green’s Dictionary of Slang

drop off v.¹

1. to die.

1771		Foote Maid of Bath in Works (1799) II 208: A few feeble fellows that dropt off with the leaves in October.
1804		H.H. Brackenridge Modern Chivalry (1937) Pt II Vol. I Bk II 442: There are chimney sweepers, who think they will all go to pot, when they drop off.
1839		Carlisle Jrnl 2 Nov. 4/2: If the old woman should drop off, I should not be very much surprised to see these two farms thrown into one.
1844		New Sprees of London 21: This crib is kept by a notorious face maker, named Bob Dorkings, the only surviving branch of a family that have all dropped off suddenly, at hot roll time.
1861		(con. 1840s–50s) H. Mayhew London Labour and London Poor II 468/2: All my friends is dropping off. I’m fifty-five, and they was men when I was a boy.
1890		Sporting Times 15 Mar. 1/5: My physician says I am liable to drop off at any moment with heart disease. He gives me only a couple of months to live.
1924		E. Pound letter 26 Dec. in Paige (1971) 192: On further considerations, better not send copy Cantos to Hardy. He may drop off at any moment.
1930		H. Ashton Doctor Serocold (1936) 149: You must be pretty busy to-day, with your partner dropping off suddenly like that.
1936		L. Pound ‘American Euphemisms for Dying’ in AS XI:3 199: Dropped off.

2. to retire.

1867

H.L. Williams Ticket-of-Leave Man 20: He dropped off a month ago and was on the pension list ever since.

3. to kill.

1930

‘Armitage Traill’ Scarface Ch. iii: Spingola had been about the first of the city’s gang leaders to enforce his power with a gun and his being dropped off so suddenly was most disconcerting to the other leaders.

SE in slang uses

In phrases

drop off a style (v.)

(W.I.) to lose one’s sex appeal.

1995

Francis-Jackson Official Dancehall Dict. 17: Drop-off-a-style to lose one’s sexiness, figure, etc.

drop off the hook(s) (v.)

to die.

1840		Era 20 Dec. 5/4: It’s five weeks [...] since auld biddy Hoolijan tuck herself off the hooks .
1859, 1860		Hotten Dict. of Modern Sl. etc.
1864, 1867, 1870		Hotten Sl. Dict.
1890		Boston Wkly Globe (MA) 9 Aug. n.p.: ‘I onlly want to make sure ye don’t drop off the hooks when I show ye’.
1895		Crowe Aus. Sl. Dict. 37: Hooks, ‘dropped off the hooks,’ is dead.
1936		L. Pound ‘American Euphemisms for Dying’ in AS XI:3 199: Dropped off the hooks.

drop off the shopping (v.)

to defecate.

2005

P. Howard Curious Incident of the Dog in the Nightdress 166: I’ve got to drop off the shopping [...] and I have to pass her old man’s study on the way to the jacks.