Subverted: Emperor Evulz puts out an arrest warrant for Velvet, but instead of hiding out, she confronts him. Or she is openly granted asylum by another kingdom.
Double Subverted: ...But the attack fails, or she hates being an exile, so she returns as a fugitive.
Parodied: Most of the nobility is "in hiding," but everybody except Emperor Evulz knows exactly where they are. May be the result of their Paper-Thin Disguise: the nobility walk the street wearing masks or odd hats, which prevents the Emperor or his Mooks from recognizing them. The aristocracy is based in "The Hidden Grotto," which is marked on every single map.
Zig Zagged: ???
No member of the nobility is ever on the run.
The nobility is too proud to run. If they lose a power struggle they either engage in a last stand or commit mass suicide.
Enforced: Velvet's royal background is being saved for The Reveal, so the writers needed some way to ensure she met La Résistance.
Lampshaded: "Don't tell me, you're a princess in hiding."
Invoked: Princess Velvet's father exiles her for a while so she can learn what it's like t be a commoner before ruling over her people.
Exploited: King Cunning hides Princess Velvet in the hope that she will later start a Civil War in a neighbor's kingdom.
Defied: A U.N. expy enforces laws that protect former rulers from having to go into hiding. Princess Velvet is able to live openly.
Discussed: "But sire, what if your predecessor's heir is living among the commoners?"
Deconstructed: Velvet is so used to living the high life that she has difficulty adjusting to life on the run; unable to hide her heritage, she is eventually discovered and dealt with.
Reconstructed: Velvet has trouble adjusting to life on the run at first, but with help from sympathetic villagers is able to overcome this, and emerges as a stronger person for going through such trials.