said by wifi4milez :

Of course it still works, unless you pull out the power plug! The content you have recorded is stored on a local hard drive, so you can access it any time the machine is booted up. I havent yet tried it with my FIOS, however it certainly worked with TWC.

said by TKJunkMail :

The DVR STB could still play existing already recorded shows if cable goes out. But only as long as the STB wasn't powered down and restarted while the cable is down. Because if you power on a DVR STB after a power outage and the cable connection is still down, it won't come up far enough to play back existing recordings.