Green’s Dictionary of Slang

1. to steal small coins.

1864, 1867, 1870		Hotten Sl. Dict.
1873		Sl. Dict. 290: Sift to embezzle small coins, those which might pass through a sieve ― as threepennies and fourpennies ― and which are, therefore, not likely to be missed.

2. to empty out a wallet or purse to identify and extract cash and valuables; thus sifting n.

1859

Matsell Vocabulum 80: sifting [...] emptying purses or pocket-books for the purpose of examining their contents, is called sifting.