Safe/not safe at home/no call made

[Coach B]

A runner seemingly scores at home with no throw to the plate, but does not actually touch home.  The defense assumes he scores, and gets the ball to the pitcher and prepares for the next batter.  The runner (who "scored") simply walks to his dugout, and the next batter gets ready to hit.  The plate umpire says nothing and never signaled a safe call, and never signaled out as the runner walks off.  Everybody in the park thinks he scored.  What's the call?  

[Velho]

17 minutes ago, Coach B said:

What's the call?

There is no call unless and until the defense appeals that the runner missed home plate. That appeal has to happen before the next pitch (or play depending on the ruleset).