no easy way out

The owner upstream (I assume your cousin is upstream) has a responsibility for the safety of the owner downstream. So if he tears it down now, as long as there is water running downstream, he will end up building a new wall.
Or he can try to start digging previous owner's responsibility and possible lawsuit. As long as the previous owner didn't built the wall, it's a tricky thing to prove he/she knew the problem.
The wall has no permit, but there is a chance it can be corrected by fixing it. Again he has to talk to the engineer and the town.
Any of this is expensive. If your cousin can't afford it, he should get his insurance company involved now in case there is a liability lawsuit. But as to the wall, it's his full responsibility and the insurance won't fix it.