Why does a complete discharge destroy a Li-Ion-Battery?
In a Lithium ion cell, the anode material can dissolve in the electrolyte, and then on recharge, precipitate in the midst of the electrolyte and insulating membrane, short-circuiting the cell. Further, the cathode material can release oxygen, which migrates away and does not get reincorporated on charging.

Another problem with most secondary (storage) cells, Pb-acid as well as Li, is physical destruction of the structure on over-charging and under-charging. During the charge-discharge cycle, there is some change in volume of the electrodes, which causes them to spall, shedding pieces of the active material. This leads to loss of capacity and sometimes a short-circuit.

Even a fully charged cell deteriorates gradually... but increased discharge increases the growth of precipitates. Li-ion cells self-discharge about 2%/mo, (half-life of ~2 years), so a charged cell is quite stable, with no perceptible growth of whiskers or precipitate for years.