Formerly the persons claiming the benefit of clergy were obliged to read a verse in a Latin manuscript psalter: this saving them from the gallows, was termed their neck verse: it was the first verse of the fiftyfirst psalm, Miserere mei,&c.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Neck Stamper * Neck WeedNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes