Green’s Dictionary of Slang

1. the human back.

1858

A. Mayhew Paved with Gold 169: ‘I’ll have yer down on “the last card of your pack” as soon as I’ve laced my “German flutes”’ — meaning thereby that when his boots were arranged he would throw Philip on his back.

2. dismissal from employment [= sack n. (2a)].

1943		R. Llewellyn None But the Lonely Heart 179: I got the sack. Last card in the pack.
1969		S.T. Kendall Up the Frog.