What happened? There's only one stone, no date.
Only a few fortunate ones were buried at all. It happened so fast, families were buried together. Dates became unimportant as all systems broke down. Finally, there were no more armies or fighting. Only starvation, contamination and lingering death.
World War III is a pivotal point in Earth's history, which resulted in an event 25th century humans refer to as the Holocaust.
Occurring later in 1987 CE, William "Buck" Rogers escapes a calamity that befell his planet and time aboard Ranger 3, despite his attempt to remedy it (BR25: "Awakening", "Testimony of a Traitor"). Sometime during 1987, Hieronymus Fox creates his own cryo chamber prototype, using it to preserve himself (BR25: "Cosmic Whiz Kid").
In the time following, humans left—or were taken from—Earth and spread out across the stars, either singularly or co-habitually colonizing various planets. This process occurred in the intervening centuries betwixt the 20th and the 25th, resulting in various divergences and sub-cultures to the Terran genome (BR25: "Planet of the Slave Girls", "The Plot to Kill a City", "Time of the Hawk"). There are also indications that other cultures, such as the bird-men, left Earth well before any "World Wars" befell the Terrans by their own hands (BR25: "Time of the Hawk").
Returning home in the year 2491 CE, Rogers discovers that his parents and siblings are buried in Old Chicago, their graves marked with a singular family stone. Dr. Theopolis informs Rogers that the war caused a great calamity to befall the entirety of Earth, with the survivors having to deal with starvation, contamination and lingering death (BR25: "Awakening").