This has happened to me twice now, so I decided to document it here:

I have an older laptop and the battery doesn’t charge anymore, so the power has to be plugged in. If it is unplugged, it loses power and turns off. This seems to cause the user folder to become read only, which then causes system instability and when it is rebooted, the system will boot into the BusyBox command line.

If you are booted into BusyBox instead of Linux Mint, you’ll see a command line. First type exit. A disk error will be detected, automatically run fsck, and then tell you you have to run it manually.
fsck /dev/sda2 -y

Note: Your disk may not be sda2, so enter whichever disk displays the error after typing exit.

Type reboot, once fsck is complete, and your computer should boot normally.