There are circumstances, such as in the context of New York's products liability or premises liability laws, where you can be held liable for a dangerous condition or accident, even though you had no active role in that occurrence. (For more on this topic, you can download the free e-book, "Why There Are So Few Successful Defective Products Lawsuits").
But that doesn't necessarily mean you have no recourse - even if you did not have a contract provision whereby the actively negligent party agreed to indemnify you (or, in legalese, "contractual indemnity").
And the reason is straightforward: the doctrine of common-law indemnity.
New York's courts have summarized the doctrine as follows:
"[I]n the absence of an express contractual agreement the courts recognized an implied contract of indemnity…in favor of the wrongdoer who has been guilty of passive negligence…against the one who has been actively negligent." Rock v. Reed-Prentice Div. of Package Machinery Co., 346 N.E.2d 520, 522 (N.Y. 1976).
"In the classic indemnification case, 'the one seeking indemnity had committed no wrong, but by virtue of some relationship with the tort-feasor or obligation imposed by law, was nevertheless held liable to the injured party.'" Glaser v. Fortunoff of West bury Corp., 71 N.Y.2d 643, 646, 529 N.Y.S.2d 59, 524 N.E.2d 413 (1988), quoting D'Ambrosio v. City of New York, 55 N.Y.2d 454, 461, 450 N.Y.S.2d 149, 435 N.E.2d 366 (1982). Common-law indemnity thus permits one who "is held liable solely on account of the negligence of another…to shift the entire liability to the one who was negligent." D'Ambrosio, 55 N.Y.2d at 462, 450 N.Y.S.2d 149, 435 N.E.2d 366…. Miloscia v. B.R. Guest Holdings, LLC, 928 N.Y.S.2d 905, 919 (N.Y. Sup. Ct. 2011).
There is an important caveat to this rule, however: the one seeking indemnification must bear no fault for the incident whatsoever.
To that end, New York's courts have stated that where "the party seeking indemnification was himself partially at fault, the courts of [New York] State, and throughout the Nation generally, [have] refused to imply a right to…indemnification against another who played an effective role in causing the damage." Rock, 346 N.E.2d at 522; Trustees of Columbia Univ. in City of N.Y. v. Mitchell/Giurgola Assocs., 492 N.Y.S.2d 371, 375 (1st Dep't 1985) ("[A] party who has itself actually participated to some degree in the wrongdoing cannot receive the benefit of the doctrine.").