suretyship
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.
as a man desperately swimming drowns him that comes to help him, by suretyship and borrowing they will willingly undo all their associates and allies […].
Where it comes from
From surety + -ship, possibly a partial calque of Middle English borweship (“suretiship, borrowship”).
Adapted from the Wiktionary entry suretyship (CC BY-SA 4.0).