More than 3 million men fought and 530,000 men died in the conflict between North and South. Pvt. Mose Triplett joined the rebels, deserted on the road to Gettysburg, defected to the Union and married so late in life to a woman so young that their daughter Irene is today 84 years old—and the last child of any Civil War veteran still on the VA benefits rolls.

Ms. Triplett’s pension, small as it is, stands as a reminder that war’s bills don’t stop coming when the guns fall silent. The VA is still paying benefits to 16 widows and children of veterans from the 1898 Spanish-American War.

The last U.S. World War I veteran died in 2011. But 4,038 widows, sons and daughters get monthly VA pension or other payments. The government’s annual tab for surviving family from those long-ago wars comes to $16.5 million.

Spouses, parents and children of deceased veterans from World War II, Korea, Vietnam, Kuwait, Iraq and Afghanistan received $6.7 billion in the 2013 fiscal year that ended Sept. 30. Payments are based on financial need, any disabilities, and whether the veteran’s death was tied to military service.