In or before 2366, John Doe and three other Zalkonians fled their homeworld in order to undergo the complete metamorphosis of their species from corporeal to non-corporeal beings. All but John Doe were hunted down by Zalkonian authorities before they could finish the transformation, however.
When the crew of the USS Enterprise-D found a Zalkonian escape pod on a planet in the Zeta Gelis Cluster, with a badly wounded John Doe on board, they were able to reconstruct the course of his ship, back to Zalkon. At the time, Zalkon was on the Enterprise's intended course, and was already projected to be reached within 3 weeks, during their star charting mission. (TNG: "Transfigurations")