It depends. With a fully-insured policy, your family will typically receive full death benefits regardless of whether your plan was paid up. However, even fully-insured plans are contestable in the first two years. In cases of suicide or fraudulent information on the application, full benefits will not be paid.
In general, accidental death is fully covered even by limited benefit insurance policies. If the policy has no insurance coverage, your next of kin will receive the current death benefit of the plan. If any expenses still remain, the surviving family members must cover the cost.