It depends but usually nothing too bad.
Most processes that prompt this kind of message can be recovered from terminating abruptly if the process was well-designed. The software will journal its progress and if it fails or is interrupted, will be able to roll back its incomplete changes. Most OS updates are like this. This is usually followed by another long-running “don’t shut off your power” process at next boot when it cleans up and checks system files.
Some processes really don’t take this well, though.
Power loss when running something that modifies the filesystems or partitions on disk can result in data loss or a system that won’t boot. Power loss while updating firmware is very bad. While some fancier devices keep a firmware backup, this is rare and without it, the device can be very hard to repair.
At the end of the day, it’s going to depend on what kind of operations are being done and how much care has been taken to make failures recoverable.
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