2011 iMac using macOS High Sierra 10.13.6 frequently completely shuts down while in Sleep Mode

To restart my iMac I have to unplug it from the power source before fully rebooting it--WHAT'S GOING ON?

That's an indication of a bad power supply.  Had the same problem occur with a late 2014 27" iMac. Had to unplug the power cord before it would reboot.  It was under warranty but took 3 trips to the Genius Bar and several sessions with Apple engineers via phone before it got fixed.  

They wanted to make sure the problem wasn't software related and finally had me erase the drive and reinstall the system without migrating any of my data over from Time Machine.  When it kept crashing with a new, pristine system they went ahead and replaced the power supply. 

Make sure you hav a current backup (a clone to an external HD is very good for this type of restore) and make an appointment at the nearest Apple Authorized Service Provider (AASP). Have them test it and, if necessary, erase the HD and install a new, pristine system.  Might save you a couple of trips.  

Since it's not in warranty (Apple considered this model Vintage and won't work on it unless you're in California or Turkey. Yes, that's right. It's not a typo. Vintage and obsolete products - Apple Support) you can take it into an AASP and just have them replace the power supply right off the bat to save time. It's you're call. Or you could erase the drive, install a new system without migrating your files to it and see if it still crashes. That will definitely prove that it's not software related. If you clone the drive before hand it will be easy to boot from the cloned external drive and clone it back to the iMac's internal drive or migrate from your Time Machine backup.

Please post an EtreCheck report of your system and we can look for any obvious issues. Please click the link, watch the slideshow to learn how to use the tool and download and run the free version of the app and then post the complete report it produces as your reply to this message. 

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Replacing a power supply does not affect the HD or any data, however it SHOULD NOT be done by you as it can be fatally dangerous if you goof up. Take it to your local Apple Authorized Service Provider to have the work done, assuming they can get the parts. I am putting in that provision as the computer is considered vintage and parts may not be available, however then again they might be.