[Sprint  Galaxy Note 4 Q&A, Help & Troubleshooting] samep:
There's lots of theories of what's happening, that's true. But I think evidence points directly to the eMMC.

You can find how to videos on YouTube for replacing eMMC chip on main board or just main board replacement. There are many places on Amazon and eBay to buy main board replacement for Note 4.

I asked my local uBreakItiFixIt for an estimate on main board replacement. They don't stock eMMC or main board but gave me a $10 labor quote for board replacement that I would bring in myself.

There was a poster that was trying to localize the issue through a developer online. Sent his phone to him to flash the recovery, claiming the partition was corrupt but he got his phone back with same issue. I do believe many happy ending threads in our forum are incomplete.

There was a thread in another site that had numerous phones exhibiting eMMC failure that were Odin flashed with PIT loaded, repartition with PIT, nand erase all and stock tar loaded all at once and I don't think there was a happy ending anywhere to be found where reports after flash were followed up.

That suggests it's not corruption but component failure. And also suggests this shouldn't be happening with normal flash or update. I think the update places a burden on weak components is where the correlation to update is coming from.

From my own experience, only few issues have happened that a reboot wouldn't fix. Twice over the entire life of my phone- picked up on launch day as a pre-order and kept in continual service since-, I've had to Odin TWRP because the phone wouldn't boot into recovery from system boot, when commanded.

The times I've flashed ROM again or wiped cache and dalvik-cache and rebooted were mostly my doing that caused unexpected results. I also crashed marshmallow twice early on while modifying stock and wasn't sure how I did that but all in all, I think I'm to blame for mistakes rather than the phone or OS updates. My phone has remained healthy but I've also replaced the battery frequently.

How's your battery? If you can Odin stock tar successfully, I'd try it again but only with a fresh battery. I'm suspicious of replacement battery's shelf life if ordering a replacement battery has it arriving with very low capacity. Research has shown batteries last longer for users when they're stored at 50% capacity and maintained at that capacity. But they're low drain batteries but imagine they could have made in bulk when Note 4 was first manufactured. If left to drain and not maintained, you may not get a year's worth of normal use from that battery. The original battery received new with these phones were notably failing at 12 months. Also depends on use. Others may fail sooner; they're rated at 500 full charge and discharge cycles. Depending on use, they may not last as long as rated or get the cycles used up prior to a year. They can become erratic and unstable at that point, whenever that is.

Nonetheless, if you want to try procedure I described earlier, a post is linked below for reference. Consider also that the more you flash a failed or intermittent eMMC, you're more likely to induce its demise to permanent or persistent failure; unusable.

https://xdaforums.com/showthread.php?p=70181377

As far as EFS partition, I wouldn't try to restore a backup if replacing eMMC or main board. Phone should activate easily if you're a Sprint subscriber. Just Odin stock tar.