I think you are assuming such a case involves the fundamental legal principles of equity and estoppel - even if you don't recognize them by their technical names.
Basically, estoppel is a common law doctrine which prevents a party (ie, the debtor) taking a certain course of action and then revoking it after someone else (ie, the lender) has relied on such information or actions and the revocation would be to the latter's detriment.
For example, suppose an insurance adjuster tells you to take your car to a garage for repair after an accident and then the claims manager calls next week to tell you their adjuster made a mistake and you're not covered. Nevertheless, the insurance company would be "estopped" from reneging on the repair even if there was really no coverage. Their agent led you believe you were covered and so the insurer must pay irregardless because of the "vicarious liability" of their agent/employee.
For a more comprehensive explanation, see the Wikipedia article below.
http://en.wikipedia.org/wiki/Estoppel
However, what about the case of a person who admitted a loan and kept on making payments on it, only to realize it wasn't his at some later date? Would the the legal principle of equity and estoppel prevail? (Stupidity certainly would, but that is another matter.)
Contracts can be either verbal or written. Of course, virtually all contracts are written but that still doesn't mean verbal ones are not valid; only that they're more difficult to enforce in court due to the lack of tangible evidence and certainty of terms. The loan creditor, in this case, might argue a valid contract had been created by the verbal admissions of the debtor and also by his actions of making payments.
First, the claimed loan agreement would not have been a valid contract since it lacked the essential elements. One such element is a "genuine intention" (or "exchange of consents" in Quebec). It requires a meeting of the minds of the 2 parties about all material details of the agreement before contracting. Obviously, there was no such thing. Thus any claimed loan agreement by the creditor, verbal or written, would be void from the beginning.
It might appear the creditor could invoke "estoppel" or "equity." Both legal principles involve how a valid contract is interpreted when there is an ambiguity or dispute about the terms. Obviously, it assumes a valid pre-existing contract, which doesn't occur here.
Ray
PS: (The legal principle of "equity" mandates that basic fairness and the reasonable expectations of the parties take priority over the actual details of the contract when their literal interpretation would be so onerous as to violate basic rules of fairness. For an example of what the courts consider "an abuse of right of contract" see the famous case of Banque Nationale du Canada v. Houle, [1991]. It's Quebec Civil Code Law, but it gives you a pretty good idea.)