What are the implications of uncontrolled power-down?

In the BBB SRM, there’s this warning,

We recommend that you use this method [pushing the power button for 8 s] to power down the board. It will also help prevent contamination of the SD card or the eMMC.

However for the application I am interested in, I can’t trust that the mains power won’t fail or that my users won’t simply remove the power cable at some point.

What are the possible consequences if they do this? (Board or uSD card needs to be re-flashed?)

Are there well-known solutions for this?
I would be designing a new cape for my project, so hardware could be built in to that.