Can you refinance your car that is about to be repossessed?

If they started that process they are done. The only thing you can do is get money elsewhere and give them cash to get it back if you can get the money. There will be a penalty and you will have to pay for the repossession even. You can do a voluntary surrender if you can't keep it which looks better. If you let them take it, no one else will give you a car right away so you have to play ball with them.