(The only caveat is with a few creditors that I’ll cover later).
Even if you don’t reaffirm the car loan (or a home loan/mortgage for that matter), so long as you pay off the balance in full, you will own the car. You’ve fulfilled the contractual obligation, and the lender has no option but to remove themselves as a lienholder on the title and send the free and clear title to you. So let’s say you don’t reaffirm on your car loan but keep the payments current. You pay it off about two years after the bankruptcy has been discharged, making current payments the whole time. What happens? The bank sends you the title. It’s that simple.
However, some creditors require that you reaffirm on your vehicle or they will repossess it anyway. You will know about this in the first three months of the case. It won’t be a surprise 6 months after you’ve filed. I discuss this reaffirmation problem/requirement here: http://robertspaynelaw.com/myutahbankruptcyblog/2014/03/27/do-i-have-to-reaffirm-my-car-loan-to-keep-my-car/