When you do not reaffirm an auto loan after BK the following things happen, one the auto loan will show paid in full due to BK and zero balance, any further payments will be considered voluntary and will not be reported to CRs and at anytime the lein holder could decide to repossess the car (probability low since it would cost them more to do this). Voluntary payments will not hurt nor help your credit score. Basically you are paying rent on your car.
I know this because this is what I did with my car. I car shopped and was finally after a lot of discouraging experiences with a different car dealers, I was able to get a new 2015 Honda Civic Coupe LX under MSRP financed through Honda, my CRs were in the mid-400's and so my APR is high but I will be able to refinance in 6-12 months at a lower APR. Once Honda reported my account to the CRs, my score did go up a little bit but once I start paying on time my scores should jump up even further.
Once I got the contract signed and had my new car home, I contacted my lein holder and asked them to arrange a pick up. It took a week or two but my car was picked up and will be sold sometime in early to mid January. I will not be liable for any amount owed nor will it show up as a repo since it was paid in full due to the BK so don't let any dealer try a trade in deal especially if you are underwater with your current auto loan.
If you are underwater (which you probably are since it is a '14 model), you would be better off shopping for something different. Just make sure you don't get into the same predicament (being underwater). We were approved by Capital One for a car loan at 9.65% about 6mos post discharge. At some point I may look at refinancing, but am content with that rate at this point.
I did find out, DCU is not BK friendly on the car loan side. I tried with them and was declined because of the BK7. After a year or 2 it might be different.
Anytime you drive off a car lot with a car, the car depreciates. The amount of depreciation is based on numerous factor, it is like a black science trying to figure it out. Try to get the best deal you can and before you even start shopping do your research.
Some CUs will not finance an auto loan if you have had a BK less than year ago. Ask CUs about their policies concerning auto loans and BK before you apply. I was able to get financing through Honda Financial but it is a high APR but in about 6 months I should be able to refinance through Capital One with a lower APR and in another 6 months I should be able to finance through my local CU with an even lower APR.
Edit: If I make 1 year of on time payments with Honda Financial, I will be eligible for those special deals Honda keeps offering. I am finding that you have to wait at least a year before you are able to refinance especially if you have burnt Capital One. YMMV