Given that the monitor/screen is appropriately attached/connected-in — that is, the cable is not partly inserted in and receiving partial visual connection — and that the drives really Aren't active — such as doing a restoration (must know what the system is used for, scheduled tasks, etc. ), and...
Power cycling (or unplugging) a computer seldom corrupts other data on the machine these days, with the exception of any data that is actively being written (that may include the last load times of files — such as during backups).
The failure of Operating System and Hardware Vendors to test the power cycling event during Validation is much too often.
Now comes the actual question: what were you doing when it happened? Was there anything else going on? Is the video being taken over by a program? (Think of a screen saver.) Is there malicious over-the-internet software?
Check system events in the BIOS once it has been restored, assuming the computer logs are still there. Then go through the ‘system logs' for system occurrences. Make sure there are no hardware issues. And so forth.
When a computer blue screens (i.e., displays the Windows Blue Screen of Death), it implies that the operating system has recognized a problem and has shut down to avoid data corruption or hardware damage. What you're seeing during the bluescreen is the operating system keeping track of what transpired. So, no, shutting down a computer during a BSOD will not create problems since the machine has already been partly shut down from a software perspective.
Because the only method to normally get out of a "BSOD" is to power cycle the computer, you have little choice but to do so. The OS is no longer operational after "BSOD" occurs. As a result, turning it off has no effect. If it's corrupted, it's already been harmed by whatever produced the "BSOD" in the first place.