ANYTIME ANYONE cosigns ANYTHING, one should be prepared to take on that payment. My father cosigned some things for my brothers, and under some circumstances I would cosign some things, but always with the full understanding that I could be taking on the whole load.
Auto loans are often cosigned by relatives, particularly parents, and I don't see any reason not to do so. It is a secured loan, and it is usually for a short period of time for a small enough amount that it is usually doable. If you have a kid who needs a decent car and doesn't have the cash to pay it, but has prospects and the car can make a difference, I wouldn't see any reason not to cosign unless you can't afford it if anything should happen to your kid and if you simply don't want to do it.
School loans are a whole other thing. A big problem with them is their magnitude and duration, so calculating the affordability of them can have a lot of probability in them. THe private loans are oftne not flexible in their terms. Better to take a PLUS DIrect Parent loan and make a separate agreement with the kid in most cases. That way you don't fool yourself on who is truly on the hook, and if you or the student should die, the loan is forgiven. ALso the hardship provisions are more flexible.
But ANYTIMe you cosign, you have to be fully aware that it's just like taking out the loan yourself if anything should go wrong with the person for whom you cosign, and the reason a cosigner is being asked for is because it is probable that something will.