No, if you only have liability then your insurance company would not normally be obliged or responsible in anyway for helping you obtain payment from the at-fault party or their insurance company.

With only liability coverages your insurance policy covers you when you are at fault and damage another person (bodily injury) or personal property (property damage). If you are not at fault then your liability coverages would not be used or claimed against and thus your insurance carrier would not be involved in the claims process.

If your car was totaled due to the fault of another driver it would be your responsibility to make a third party claim against that person's liability coverages. If at-fault party was not insured or their insurer denied your claim for your totaled out vehicle then you would need to find out what your legal rights are in your state. In most states you could take the at-fault driver to court to seek a judgment against him or her for the damages to your vehicle, in this case the total loss of your car.

If you had physical damage coverages, collision and comprehensive, and you decided to make a first party claim against your own coverages instead of the against the at-fault party's insurance policy then your insurer would not only settle with you for the actual cash value (ACV) of your totaled vehicle but then likely subrogate or go after either the at-fault party or their insurer to recoup the monies they paid out for your claim.

Without having physical damage coverages on your automobile then your own insurer would not normally be involved in your claims process against the at-fault party since they are not paying out money on your behalf that they need to reclaim. If you need help filing your claim against the person that caused the accident that totaled your vehicle then your insurance agent may be able to offer advice but you would be responsible for making the claim and settling with the at-fault party.