Lifting much of my answer heavily from Wax Eagle's answer here:
From MLB rule 5.09(c)(2)
[The runner is out on appeal when] With the ball in play, while advancing or returning to a base, he fails to touch each base in order before he, or a missed base, is tagged.
This basically means that a runner is considered safe after they've rounded first base without touching it, that is until either he or the base he missed is tagged before he returns to it and the fielding team appeals to the umpire.
However, this specific scenario is addressed in rule 5.09(d)
Unless two are out, the status of a following runner is not affected by a preceding runner’s failure to touch or retouch a base. If, upon appeal, the preceding runner is the third out, no runners following him shall score. If such third out is the result of a force play, neither preceding nor following runners shall score.
I read this as meaning that a "missed base out" (i.e. missed the...