My daughter is buying a second car from a private seller, I would like to know if there is any way to find out if money is still owed on the car by the owner before she buys it?:

If the vehicle is paid off, the seller should be able to show you the title.

Do you suspect the seller has used the vehicle as collateral and has an outstanding lien? If so, keep shopping.

You could check with Motor Vehicle. They would have the record of any lien holder, at least they do where I live.

My daughter is buying a second car from a private seller, i would like to know if there is any way to find out if money is still owed on the car by the owner before she buys it?:
When you go to assess the vehicle at the court house, they will not, and can not let you do it unless the title is clean, with no leins on it. Ask the seller. Most individuals will be honest with you about such a thing, but there are a lot of things to watch for when buying a used vehicle from an individual. I do that for a living, and if you need some hints on what to watch for, and listen for when test driving it, let me know I'd be glad to help you in any way I can.