We have that happen a lot here in Canada. We don't have title's so it's up to the seller to have the liens removed.
So if no one follows up then it get's left on record. All the seller need do is to get a letter from debtor (Bank) to indicate they no longer have an interest in this car. Bring that to the DMV and you will get you registration.
Your system is different than ours but your DMV must have a process to handle these sort of situations.