The same thing happens with lithium ion batteries. What happens during over discharge is that it is possible to reverse charge at least one cell in the battery. This will cause a lot of damage to the cell which is reverse charged. The reverse charging can be regarded in some ways as an extreme version of discharging the cell.
Abstr. MA2016-02 897 DOI 10.1149/MA2016-02/6/897 Cell reversal in lithium ion (Li-ion) batteries is the condition of the anode electrochemical potential rising above that of the cathode, resulting in a negative voltage measured at the cell level.
The problem comes when partially or fully discharged batteries are mixed with new batteries, thus creating a situation where the discharged cell could be reverse charged by the new cell. This is a big "no no" for primary lithium cells and could result in explosion. BAT1 in this case is the discharged cell:
It is well known that Li-Ion batteries should not be deep discharged. But sometimes they do discharge deeply. Is it OK for the device to remain in such state for a long time (and recharge again only when the device is needed again after a year) or it should be charged back as soon as possible? In other words, the battery was discharged deeply.
Yes, it is dangerous to attempt to charge a deeply discharged Lithium battery. Most Lithium charger ICs measure each cell's voltage when charging begins and if the voltage is below a minimum of 2.5V to 3.0V it attempts a charge at a very low current . If the voltage does not rise then the charger IC stops charging and alerts an alarm.
The reverse charging can be regarded in some ways as an extreme version of discharging the cell. What will happen is that new and unwanted reactions can occur in the cell. Well it kind of depends on the materials in the battery. One consideration would be the strain or rearrangement of the crystal structure of the cathode material.