My spouse died. What happens to a loan we took out together?

When two people take out a loan together, they are joint debtors. Each of you is fully and independently responsible for paying back the loan. If one of you can't contribute their share for whatever reason, the lender can expect money from the other. 

Whether as the surviving spouse you can keep the vehicle will depend on how the vehicle is registered. If the vehicle is registered in your joint names, then it would pass outside of the estate. Ownership can transfer directly to you as the other joint owner. And the vehicle would not be subject to the claims of creditors.

If this is the case, as the surviving joint owner you must attend at an Autoplan agent with the death certificate, the vehicle registration, insurance, and licence plates, and have the vehicle transferred into your name alone. ICBC has a checklist for estate transfers. Note that a jointly owned vehicle must be transferred into the name of the surviving owner before it can be sold to a third party.

If the vehicle was registered in only your spouse's name, then it would go into their estate. The personal representative would be liable to keep up the car payments. (They should reimburse you for the car payments you made after the deceased passed away.)

The personal representative would distribute the estate according to the instructions in the will (or under the law if there was no will). If your spouse owed money to creditors, the creditors can make a claim against the estate. The fate of the vehicle will depend in part on the amount of debts and other assets in the estate, and in part on who is entitled to a share of your spouse's estate.