No, your Gap insurance would not help with your car payments because you lost your job.
Gap insurance covers the balance of a lease or loan when a covered loss has occurred and actual cash value (ACV) has been paid out by a primary insurer.
A covered loss in this situation usually requires the vehicle being declared a total loss such as the vehicle being stolen or an accident where the damages were so severe the car is totaled out. Either way the primary insurance has paid out the actual cash value ACV for the automobile.
Gap pays out the difference between ACV and the balance of the lease or loan. Without the ACV being paid out Gap insurance does not normally pay out thus if you were fired from your job and need help with your monthly car payments this situation would not qualify for Gap insurance coverage being used.
[Let CarInsurance.com help you find affordable auto insurance now.] Gap insurance is not set up for this type of situation and thus does not pay our any money for you to continue to make your car payments while you are out of work. Also keep in mind that if you are out of work and are unable to make your car payments and are in an accident where your vehicle is declared a total loss, Gap insurance will not pay for any overdue lease/loan payments that you missed if they pay out on a claim.
There is Payment Protection Insurance that could help you out if you are unemployed. Some finance companies bundle this type of insurance to those paying off a lease or loan. Payment Protection Insurance will normally pay your monthly payments on any motor vehicle finance agreement, mortgage, or any type of loan if you become unemployed or cannot work due to accident or illness.
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Payment Protection is normally paid monthly, at the same time as any finance repayment. Not everyone is eligible for it; if you are long-term sick or self-employed, you probably may not be able to obtain this coverage.
If you are interested in this type of coverage go over the policy to make certain what it would pay if you were out of work. There may be a limit to how many payments are made under this plan. It may also not kick in immediately; you may have to find the money for the first three months after a change of personal circumstances (out of a job or illness so you cannot work).
You can check with your state's insurance regulator to get information on the type of job loss insurance your state has available to cover your car payments if you become unemployed and where you could obtain this type of coverage. | 
