How about having the insurance company declare the vehicle they were driving a total loss? Would your character square his or her shoulders and get on with it? Burst into tears? Observe a moment of silence for Walter (or other name)? For that matter, is your character the kind of person who names inanimate objects like cars?
When looking for a replacement vehicle, what is most important to your character? Color? Safety? Potential for attracting love interests? The sound system (my personal favorite)? Price? The carbon footprint?
Does he or she test-drive? Does your character bargain or just pay the sticker price? Is his or her credit history good enough to get a loan? Or is your character paying cash on account of having just won the lottery/inherited a great deal of money/insurance payout will cover the whole thing?
Would your character just chuck it all and buy a bicycle?
If you're writing about a time before automobiles were commonplace you can ignore this entire post, or have some fun with it and think up insurance rates and policies for horse/covered wagon/chariot/camel collisions. It may become terribly important for your characters to know which of the local blacksmiths and wheelwrights provide free estimates.
I'm afraid that's all I can offer today. Here's hoping neither you nor your characters really need to deal with this