My hypothesis of what happened to Miley Cyrus:
The Master: THIS GIRL, MILEY! SHE MAKES TEENAGE GIRLS THINK IT'S OKAY TO BE DIFFERENT. WE CAN'T HAVE THAT. DALEKS, GO EXTERMINATE HER.
Daleks: EXTERRRMMINATE.
Lady Cassandra: WAIT! She's famous, people would notice.
Master: Good point...
Daleks: Exterminate???
Master: Not yet....
Everyone: ...
Master: I GOT IT! WE'LL SEND A ZYGON TO COPY HER, TAKE HER PLACE AND RUIN HER NAME
Cassandra: THAT'S A GREAT IDEA!
Master: TEAM ANTI-CYRUS... GO!
Daleks: EXTERMINATE
Zygons: COPYIATE.
Cassandra: MOISTERIZE ME!