The story
From surety + -ship, possibly a partial calque of Middle English borweship (“suretiship, borrowship”).
Etymology from Wiktionary, CC BY-SA 4.0.
suretyship
Today it means: An accessory agreement through which one binds oneself for another already bound, either in whole or in part, as for one's debt, default or miscarriage; the assumption of liability for the obligations of another. Full definition →