It doesn't go through the judiciary (e.g., it would if it were an an apartment and you stopped paying rent), but the owner signs a loan note that specifies that the loan is in default after missing N payments (usually after 3 months). Once in default, the bank
can repossess the vehicle, but they'd rather not since their business is lending money and anything else is a money-losing distraction. So they will usually try to find a way for you to keep the car (and keep making payments). They usually only repo if they can't contact the debtor or they can't come to an agreement.
Repossession of any kind (car, house, etc...) is typically an option of last resort for the bank after the debtor refuses to work with them or enter into other agreements that could help. They really just want to keep collecting payments from you.