This is mostly an informative post, as I have spent a few hours on the phone with Verizon and Samsung tech support regarding this issue.
This issue affects the Verizon Samsung Galaxy S4 on Android 4.4.2 and Baseband version I545VRUFNK1.
First, some info. When setting a pattern lock to this phone, it will ask to enter a backup PIN in case the pattern is forgotten. Additionally, this phone has a Kids Mode widget pre-installed by Samsung to download the actual app. Once the app is installed and setup, it will allow a child to play with the phone on any app you designate, keeping them from messing around with settings and etc. This app also requires a PIN to keep kids from exiting Kids Mode or altering it's settings.
The issue with the above mentioned info is this: if Kids Mode is active and the phone goes to sleep, and the lockscreen pattern is entered incorrectly to the point that it will ask you to enter the backup PIN, the backup PIN you created WILL NOT WORK. An error message will appear stating "you have attempted to unlock the phone unsuccessfully X times, you have X times left before a factory restore is performed." Once the last attempt has been reached the error message states this feature can be turned off by going to Settings > Lock Screen > Auto Factory Reset. The additional issue here is that this menu setting does not exist. After ten failed attempts to enter the correct PIN the phone will erase the SD card and perform a factory restore.
This issue ONLY occurs when Kids Mode is installed, is active, and when there is a pattern and backup PIN set for the lockscreen. I was able to reproduce this issue six times with Verizon tech support over the phone.
Verizon did send a replacement but unfortunately this issue occurred with the replacement as they were on identical Android and Baseband versions. Verizon got me in touch with Samsung tech support and they are going to repair the phone for me. My assumption is that they will reflash with a previous version of Android, or newer. Won't know until the phone returns.
If you wish to see a video of the process, check it out here.