I think you are confusing these with Li-ion cells which most certainly do get damaged from excessive discharge. The only way this situation can really harm NiMH is if you have multiple cells in series and one gets discharged so low that the other cells partially charge it in reverse. I had that happen once with a defective flashlight and it damaged one of my Eneloop AAA cells.
Nope, I was not thinking LiIon. I was thinking AA/AAA NiMH. But I did consider going-negative and going low-voltage as the same thing in what I wrote. There is a difference between the two, so my treating it as the same is probably wrong. Good to be more precise here.
You have two options:
A battery which is old, degraded or damaged may self-discharge down to zero in storage, so that when you measure it it has no voltage. From this you would draw a conclusion that the battery is probably bad and discard it, especially if it had a good voltage when stored.
On the other hand, a good battery may be discharged down to zero by a device it is installed in. This says nothing in itself about the battery, it just says the battery has been mistreated. You may charge the battery up again and it may be fine.
A third option is you may intentionally discharge a battery to zero volts and leave it that way. In the case of NiCd chemistry this is believed to do no harm. In the case of NiMH the situation is less clear. Some people have discharged Eneloops to zero volts and stored them that way for a considerable time, and on later testing found no loss of performance. Other people have claimed otherwise. So it is hard to draw a conclusion.
In my own experience, occasionally draining an Eneloop down to zero volts does not seem to be a problem. So I do not worry too much about it.
Your option 1 and 2 are really saying that the battery is bad and low/negative are just indicators of damage, but the damage was caused by other reasons such as age. If I understood you right, I can agree with what you said.
Your statement "... Eneloop down to zero volts does not seem to be a problem..." caught my eyes and it is very interesting. This got me thinking: LSD vs non-LSD robustness in dealing with over discharge.
May be just coincidental -
I do have better luck on recovery with Eneloop and with the Chinese work alike Tenergy Centurion brand, but I do not have nearly as good recoveries for my other batteries. The Centurion AA has nearly identical specs to the first generation Eneloop AA. So at least in my case, LSD vs non-LSD appears to have a very different characteristics when ran down to zero charge (or negative) and left in the device for extended period of time.
It would be interesting to see any studies out there on LSD v non-LSD when overdischarged. That will likely be my web-search/reading for the next few days... May be it was simply my LSD's are just newer. That would be disappointing.