What to do about a verbal contract that was never fullfiled?

If the agreement is still enforceable, then you would be obligated for any damages or losses your cousin incurred due to the failure to finish the car--such as if he lost the profit on a resale of it, you'd have to pay his lost profit; or if he had to buy a new car because the old car was never completed, you might have to pay the difference in value between the vehicles. He can most likly also recover whatever money he provided to you for the restoration. He cannot make you buy the car off him, unless that was part of the agreement; for example, that if not finished within a certain time, you would buy the car. That said, it may be better, if the contract is enforceable, to buy the car, finish it, and resell it, then get involved in litigation (a lawsuit) over who owes who how much.

However, most likely, the contract is no longer enforceable: the statute of limitations, or time to enforce an oral or verbal contract, in your state is only four years; if the transaction occured 15 years ago, then it's most likely too late to legally enforce it. (Note: the statute of limitations starts its countdown from when the breach or violation occured; in terms of determining if the statutory period has expired, the key is when was the car supposed to be finished, and therefore when did your husband violate the agreement by not completing it--if it was more than 4 years ago, its probably too late for the cousin to enforce it.) In this event, you'd still have to return the car and the money you were given for the work which was never completed--otherwise, you would have been "unjustly enriched"--but that should be the extent of  your liability. Again, though, since defending a lawsuit, even when you'll win, can be expensive and emotionally stressful, if your husband could complete the car and resell for even the smallest profit--or even just breakeven--it may be worthwhile to do what your cousin suggests, to avoid litigation.