Foxfi Version 2.13.1 (Full Unlocked with Key) on Verizon with Galaxy S4 and the latest Android 4.3
I'm using Foxfi Version 2.13.1 (Full Unlocked with Key) on Verizon with Galaxy S4 and the latest Android 4.3 Verizon VRUEMJ7 update, and it all works fine. I also have a grandfathered unlimited data plan, and I don't subscribe to the Verizon hotspot feature.
I also don't get the annoying popup above saying that I'm not subscribed since I used the work-around to remove the screen-lock/password imposed when Foxfi created a certificate. I did that work-around since prior to the update to 4.3/VRUEMJ7, if that matters. The detail for that work-around can be found on the description from the developer for the FoxFi App on the Google Play store.
Prior to updating to 4.3 today I also browsed all the forums and found that one other Verizon/S4/4.3/Foxfi user like yourself reported that their Foxfi didn't work after the update. The other user like you with the issue claimed that installing the Sprint/AT&T version of the Foxfi app fixed the issue for him, so you might want to give that a try.
So, in case someone else is in the same boat as I am: I'm confirming, 100% conclusively, without a doubt, that FoxFi works perfectly on My Samsung Galaxy S4 on Verizon with Unlimited Data and no hotspot subscription.
I wish someone would have done the same for me when I was googling this question prior to accepting the OTA update.