Nedarim 33 - He paid off your debt? - You don't owe him anything!
If one person (A) makes a vow not to provide any benefit to his fellow B, he (A) is still allowed to pay off B's debts. How could it be? - By paying off B's debts, A is simply "chasing a lion away from B's property." That is, he is precluding B's creditors from running after him at some future date, and this is not a benefit.
But wait, it is a benefit, after all!? - This follows the opinion of Chanan, which we learned earlier : if one goes overseas and leaves his wife without sustenance, and his fellow provides her with money on his own, the husband is not obligated to repay.
Are there any other opinions? - Yes: those who disagree with Chanan, and say that it is a benefit. Or, if you want, I can explain that the rule about paying off debts is universally accepted. I can say that the loan of B does not have any fixed date for payment. Then the creditors will never come to B, because the "future date" mentioned above does not exist! So A really provided no benefit, and even though he vowed against B, he is still allowed to do this service.
Other things that A is allowed to do is to pay of he half-shekel obligation. Everyone had to pay the half-shekel yearly, to provide money for daily sacrifices, but even if he does not pay in the end, he still gets the atonement, thus, paying it for one's fellow is not a benefit.
Finally, he is allowed to return the fellow's lost object, because he is doing a mitzvah. If in his place they pay for the trouble of bringing the lost object, he should donate this money to the Temple.
Art: Lost by Frederick McCubbin