The Verizon variant of the second-gen Google Nexus 7 tablet, which was released back in 2013, has started receiving an update that brings Android version 5.1.1 along with a fix for the Stagefright vulnerability.
The update to the Asus-built device includes features such as Material Design, battery saver, a new recent screen, personal unlocking, and security patches among others. It also brings support for multiple users as well as Verizon's XLTE service.
Carrying software version LMY48L, the update is currently rolling out, so it may take some time before it reaches everyone. Meanwhile, you can also check for it manually by heading to your device's settings menu.