Final answer:
The death of Kurt, an active-duty serviceman killed in an accident while on leave, would likely qualify his family for the death gratuity payment. Other benefits such as life insurance from SGLI and survivor benefits through the Survivor Benefit Plan may also be available to the survivors.
Step-by-step explanation:
The question refers to the military death benefits that are available to service members who die while on active duty. If Kurt, an active-duty serviceman, was killed in an accident while home on leave, his family would most likely be eligible for the death gratuity payment. This is a lump-sum payment made frequently by the Department of Defense, in order to provide immediate financial assistance to the service member's family. It is important to note that the cause of death - being an accident in this case - generally does not affect the death gratuity eligibility, and this benefit will be paid regardless of where the service member's death occurred, including while on leave.
Moreover, the family might be eligible for other benefits, such as life insurance proceeds from the Servicemembers' Group Life Insurance (SGLI) and possible survivor benefits. The Survivor Benefit Plan (SBP), for example, is an annuity program that allows military retirees to ensure that after their death a continuous lifetime annuity is provided to their eligible survivors.