Green’s Dictionary of Slang

(US Und.) a form of deception, whereby a female beggar builds up one shoe to appear crippled, thus eliciting sympathy and alms.

1907		N.Y. Times 27 Jan. Sun. Mag. 4: The girl [...] was playing the ‘high heel game’ with a show of lameness. One of her shoes was built up, inside and out, like those used by sufferers from hip disease. [...] Struggling down a crowded street with this pitiful deformity (?) [sic] and with the aid of a crutch the money of the charitable came to her in a steady stream.
1928		M.C. Sharpe Chicago May (1929) 273: [She] was a clever woman who played the high heel (begged) over in the East Side.