A mechanical issue such as a broken timing belt that caused severe engine damage is not covered under a car insurance policy. Mechanical problems and wear and tear on a vehicle is not covered by physical damage coverages such as Collision or Comprehensive. To use these coverages on your vehicle it must be in a covered loss situation, such as a motor vehicle accident or the car is stolen, etc.
When the car has mechanical issues you would need a warranty that covered the parts of the vehicle such as the timing belt and then the engine parts it caused to be damaged with the timing belt broke. Or if you have mechanical breakdown insurance you could see if the timing belt and resulting damage from it breaking would be covered under that policy.
If the timing belt and engine are not covered by a warranty or mechanical breakdown coverage then it would leave you to pay for the repairs of the vehicle. You said it was a total loss so it would appear the cost to fix the engine is the same or more than the actual cash value of the vehicle. Since you owe a lien holder still for the vehicle you will need to continue to pay on, even if the car is not operational currently. The maintenance and repairs needed for mechanical issues is your responsibility and not the lien holder's. Your loan documents require you to pay on the vehicle until it is paid off, whether the car is in working condition or not.
If you fail to continue to pay your car payments then normally the car will be repossessed, even if it does not work. Next the lien holder will usually try to sell the vehicle to help offset what you still owe on the loan. Since the car has severe engine damage it will likely be sold for not much money and then after that amount is taken off the loan amount you will still owe the balance, even though you no longer have the car. The loan documents make you obligated to continue to pay for the vehicle.
If your vehicle is repossessed due to non-payment there likely will be the cost it being towed and stored, before it is auctioned off, that will be added to the amount you owe on the vehicle. If you do not pay those costs or the remainder on your car loan then a collection company or lawyer will likely contact you. You may be sued if you fail to pay and have then court fees also to pay out. You will also have a repossession on your credit report which will undoubtedly hurt your credit score.
The condition of your vehicle, whether it runs or not, has nothing to do with the loan requirements that say you must pay on your loan until the debt is paid off. If you do not pay for the car it will be repossessed, sold at auction and then you will be contacted to pay the remainder of your loan plus the added towing, storage, legal fees and even court costs if sued so that they receive a judgment against you.
Instead of putting yourself in this position it may be better to get quotes on the cost of repairing the vehicle to see if it is reasonable to have it fixed or not. If it is not then you should still continue to pay on the vehicle. You may see if your lien holder will allow you to sell it for salvage and thus place that money towards the balance you still owe. You will though need to continue to pay for the vehicle until it is paid off unless you want a black mark on your credit report.
A repossession or notation of failure to pay for your vehicle on your credit report will make it not only difficult to finance another vehicle in the future but can affect your auto insurance rates.
If your credit history or score will be looked to determine your cost of car insurance depends both upon your state insurance laws and an insurance company's rating system. If your state's laws allow insurance carriers to use your credit report as part of the rating system, and your insurance company in turn decides to use your credit history as one factor that they use to determine rates, than if you have a good or bad credit score could affect your insurance premiums.
Insurance companies request an insurance score on applicants because risk assessors and actuarial studies have shown that a person's credit or financial history is a good predictor of insurance claims. Actuaries have found a strong correlation between credit history and insurance claims. Also if your credit history shows non-payment or late payments it makes an auto insurance company wonder if you will pay them on time for your coverages.
If you do let your vehicle be repossessed due to your circumstances then your car insurance rates may rise. If that is the case the best thing you can do is shop around and make sure you are getting the most affordable auto insurance premiums possible. CarInsurance.com offers free auto insurance rate quotes online.