If your PS4 is having difficulty installing an update normally for whatever reason, you can opt to do so by using the Option 3 [Update System Software] in safe mode menu.

Every now and then, your PS4 might need to go into Safe Mode, especially after you’ve installed a major firmware update on your console. Usually, you’ll be able to restart your system and go ...

In Safe Mode, select the Update System Software option (it should be the third one on the list). Select Update from USB Storage Device, then select OK to confirm.

Select Safe Mode option 3: ‘Update System Software’, then choose ’Update from USB Storage Device’.

How to put PS4 in safe mode- In this guide we show you how to use the PlayStation 4 Safe Mode properly and how to fix death loop issues which might be occurring.

1. Turn off the system First, you’re going to need to force your PS4 to turn off. Hold down the power button on the front of the PS4, and wait for it to shut down.

UPDATE (11/5/14): The new v2.01 update appears to fix the widespread Rest Mode issue, so if you've downloaded that, it should be safe to put your system in hibernation again.

PS4 software update v2.01 is coming soon, and will address issues some users have encountered when powering on the system from Rest Mode — PlayStation (@PlayStation) November 5, 2014 ...

Safe Mode is a PS4 operating system mode which activates after improper power-down or any hard drive replacement. Safe mode displays a special prompt on boot and scans the PS4 hardware for errors ...

The PS4™ system starts in safe mode Select [Update System Software]. Then select [Update from USB Storage Device]. Follow the screens to complete the update.