For mobile phones, containerization is the most typical solution. A real-world example: I work for a government agency that routinely processes sensitive unclassified information. I get my work email on my personal Nexus 6. That work email lives inside an encrypted container, and I cannot copy/paste data back and forth between the container and the rest of my phone. The government "owns", manages, monitors, and secures the container and the data within, and has the ability to perform multi-pass remote wipes of the container.
Thanks for the follow up on my question. I guess I am missing something obvious - if you lose your phone and it is compromised, regardless of this container being set up, isn't the thief able to view/use your data? Once the company realizes that the device is lost, sure, they can remote wipe it (as can be done in any other case where there is no virtualization), but by then, the thief already has some (if not all) of your information.