How do you handle a tablet where all screen input and keys have become unresponsive? How do you shut down the tablet in the condition where neither screen, nor any buttons accept any input? It is possible the tablet is locked in this condition by the active software, last noted to be the Kindle app, but could be a condition caused by any active application?
My Galaxy Tab 3 sometimes freezes without capability to manipulate the restart functionality, or the application Force Close functionality. Since it is a tablet, opening its case to remove the battery is not an available capability, unlike the occasions this happens on my phone, a Samsung Galaxy S3. This is a rare occurence; it has happened twice in recent memory to my tablet. This time the active application was the Kindle app, and it may have even been so when this occured last, several months ago. This time the tablet presents a blank screen, which is active, since it emits a bare shimmer of light. The screen feels slightly warm, indicating the tablet is active. I am uncertain of the specifics of the previous occurence, finding it totally unresponsive when I took it out of my bag on a flight, after i had pre-loaded books to read on that same flight.

I am unsure this is the optimal technique, but the similarity to the last occurence led me to experiment with just letting the battery fully expire. Then plugging it in to power up and reboot into a fresh session. It appears to have restarted properly. I have not witnessed either affected memory or corrupted files so far. The Kindle app seems to have all recent books stored and available.

TL;DR - manage a way to let the battery fully discharge. Plug in and start a fresh session. Check for damaged app or files.

UPDATE 2015/06/03 - This has happened again today, again on a day when I updated my Amazon Kindle app by downloading books. Except today, I downloaded books over 2 sessions. When I recall the first instance, Christmastime 2014, this seems also plausible, since I may have refined my download and search query for some additional downloads. The second instance of this (March 2015) I am unsure about. Now that I have a refined theory, I can experiment. However, this tablet was fully charged this afternoon, so it will be a day or more before I can attempt anything in order to fully discharge the battery.