Protection of BeagleBone Black from eMMC corruption on power loss
All layers of the stack need to cooperate here.

The eMMC storage device has an integrated load balancer that needs to handle power loss situations gracefully. I'd expect it to do that, by pretending that incompletely written blocks were not written at all.

The file system needs to be able to handle power loss between block writes. The ext3 and ext4 file systems fulfill this, as they are journaled and enforce the ordering of writes so the journal accesses are kept separate from actual file system modifications.

The weak point in your setup is the package manager, which doesn't offer a good solution if the power fails during a package upgrade. Usually you should still be able to boot unless the error happened precisely during renaming files after an installation, and the files being renamed were important system files.

For almost all purposes, that window is sufficiently small that you can ignore the problem. You can shrink it more by running dpkg --configure -a and dpkg -iGROEB /var/cache/apt/archives during each boot -- these should get you back into a sane state from an interrupted update, at the expense of a bit of time, and they cannot handle cases where dpkg itself or the init system were damaged as a result.

Last but not least, you can set up a rescue system in an initrd that will check and try to repair and/or reinstall the system if needed, and anchor this in the bootloader.