If you were At Fault, then you are liable for all costs. Whether you have insurance or not does not negate your liability.
In most states if you fail to pay for the claimants losses you will lose your driving priviledges for up to 10 years or until you pay the bill which ever comes first.
If the other person has insurance to pay for their losses then you will be required to re-imburse that Insurance Company for the damages you caused, You are still the at fault party and are liable for the damages. If you don't pay the Insurance company they can also turn it over to a collection agency and it will definitely affect your credit for the next 10 years.
Basically to sum up. If you don't pay the damages you will likely lose your credit rating as well as your drivers license for the next 10 years.
If the accident is your fault, your insurance company is not going to pay out anything. If it is the other person's fault, the other insurance company will be liable.
If another person was at fault for the accident, you will need to go after their insurance company. If you are liability only, your insurance company will not pay for anything.
Its your fault
It would depend on why the car was totaled and who's fault the accident was and what time of insurance do you have PLPD or Full Coverage
Yes, If the accident was your fault, then it is your fault. Whether or not they have insurance has nothing to do with who's at fault, or who actually caused the accident.
If the accident was your fault you're out of luck. If you were hit by someone, their insurance will total your car and pay you for its actual cash value.
There is no deductible for liability claims.
An insurance agency represents the insurance company. This is the decision of the client, not the agency or the company. This has no bearing on the fault of the accident...unless they have not inspected the vehcile yet...when in most cases the vehicle is stored at a facility.
No. If the accident was your fault, you can not get money from the other person's car insurance.
the insurance of the person responsible for the accident
Yes, but proof will be necessary - determining fault. Some insurers like to mess with your head and question the "fault" and deny coverage. Get it in writing - possibly by the at-fault driver or YOUR insurance company. Here in Canada, even if you only have PLPD, if the accident is not your fault you are covered for repair, minus the deductible.