This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
Circa 3069, the Yelchin was destroyed in an event that would later be known as "The Burn". Last reported position of the starship was at coordinates 81986 mark 272139. (DIS: "People of Earth", "Unification III")
In 3189, information on the Yelchin was included with other notes of evidence about "The Burn" on a holographic note board in Michael Burnham's quarters aboard the USS Discovery. This evidence indicated the event was not simultaneous, as the destruction of the Yelchin occurred one one-millionths of a millisecond after the destruction of many other ships. (DIS: "Forget Me Not", "Scavengers", "Unification III")