What have done towards your prep?

[CharlesHarris]

A low voltage limit is subject to sulfation on the negative plate. Leaving a flooded lead-acid battery continuously on float charge for a prolonged time may boil off the electrolyte and expose the tops of the plates to the atmosphere, causing sulphation. Lead-acid batteries do not like deep cycling. Depending on the depth of discharge and operating temperature, a sealed lead-acid provides 200 to 300 discharge/charge cycles.

If you look at the discharge curve for a Lead-Acid Battery and optimistically assume that you are only interested in 0.2C discharge, at 12V there is a "tipping point" where the voltage goes from relatively constant to plummeting. At 11V it is almost going straight down. At 9V it will drop right away under the same loading current.

This means that at 12V point you have used 60% of its capacity. At 11V you are at effectively 93%. At 9V you're at 99.5%.
A battery with 0V across it has no chemical initiative any more, of any chemistry type, you will need to motivate it re-create the chemical imbalance that causes the apparent voltage and potential for current to flow. This is hard on any battery (which is why almost all batteries are built with electrodes already chemically built of the right materials to create the cell potential).

With SLA a lot of energy goes in chemical recombination of Sulphates and Sulphites, wasting a lot of energy. This results in needing excessive power to re-engage a cell that is left at 0V. Excessive power = heat. Heat = gassing. Gassing = moisture loss. Moisture loss = bad. Not to mention the higher voltage usually required makes many, many by-products on the plates, next to by-products already generated by neutering it in the first place and you're left with a AA battery with the weight and size of a BCI Group U1 SLA wheelchair battery.

Now, discharge down to near 9V, the battery will drop to 0V very quickly. You'll easily be too late to salvage it. Marine battery y manufacturers tell us to "Consider your deep cycle battery empty at 11V." Common automotive starting batteries will be damaged below 11.8V Those who keep separate engine starting and deep cycle batteries for use in their RV must take care to appreciate the difference in depth of discharge lower limits exactly for that reason.

If they will not accept that 100's of manufacturers, countless experts in the field and users alike say "at 11.8V you're not going to get much more out of it and it'll be risky to try", then just convince them with the fact that at 11V there won't be much to get any more anyway. Done. All other points moot.

The reason a car battery can be dropped to 2V and then keep working, is because that battery was at 2V very shortly, because the idiot leaving his lights on realised after a while. And because they are usually over dimensioned by a factor of 2 to 5, depending on the type and brand of a car, so a crippled one will work for a couple more years.