A new-to-me collection on Ancestry.com is titled: U.S., Headstones Provided for Deceased Union Civil War Veterans, 1861-1904. The collection consists of an alphabetical file of 3×4″ cards that were microfilmed by the National Archives.
These cards kept record of when a headstone was requested for a veteran. Here is an example:
You can see that the card included the veteran’s name, rank, cemetery location, and date the headstone was requested from the federal government.
Please note that these requests may have come years after the veteran had passed. In this case, Find A Grave shows that George Draper passed away in 1871.
You can learn more about this National Archives collection in the NGS Magazine article by Claire Prechtel-Kluskens titled Headstone records for US military veterans: Part II: Records for headstones requested from 1879 to 1925. The article can be found on page 32 of the April-June 2013, volume 39, number 2 issue.