Green’s Dictionary of Slang

fig v.

to pick pockets.

1552		G. Walker Detection of Vyle and Detestable Use of Dice Play 43: The chetor consulted with the land-lady in this case devised, that she should dally with the gentleman [...] till they might fig a link or two.
1799		Sporting Mag. Jan. XIII 219/1: The prisoner then said he had been figged at Bedfont.
1821		‘A Real Paddy’ Real Life in Ireland 209: Swan walked off to take a figging nap on the floor of his dungeon – a clean shirt and a dressing gown richer than when he came in.

In compounds

fig-boy (n.)

(UK Und.) a pickpocket or cut-purse.

1552		G. Walker Detection of Vyle and Detestable Use of Dice Play 39: Then lead they the cousin to [...] the bear baiting at Paris garden, or some other place of throng, where, by five fingered figg boy, a grounded disciple of James Elis, picked shall be his purse.
1602		W. Watson Quodlibets Religion and State 61: Practicall science inuented by fig-boyes, and men of the Bernard high lawe.
1608		Dekker Belman of London H3: Whensoeuer any notable or workmanlike Stroke is stricken, though it were as farre as the North-borders, yet can the rest of the Fig-boies here resident in London, tell by whom this worthy Act was plaid.