When one gives the impression that they'll be endorsing or working for a newer independent company, but at the last minute takes a check and signs with a larger already well-established one. The expression combines Drake, a popular hip hop artist, and Apple Music, which many rumor Drake signed with at the last minute snubbing Jay Z and his "startup" Tidal, which many are now presuming to fail.
Leona gave the impression that she'd be joining our startup as the new CTO, but at the last minute she pulled a Drapple Music Switch and ended up taking a job at Google X instead.