Here's where it gets complicated :-)
First, I totally disagree with Mr Helius. I/we have taken huge EV car packs to near 0V on many many occasions, without ANY detrimental effects.
I create V/I profiles that we need to keep within though, as the C discharge rate will de-rate a lot under ~3.2V.
This min voltage issue is mainly targeted at Lead-acid type batteries.
I often run extensive destructive tests on a new chemistry / product to check / verify their operation parameters.
Unfortunately, you're going to have to decide who to follow on that point :-)
For your situation - cells rarely read 0V00, so possibilities are - they have an internal fuse (sometimes thermal) and it is open-circuit.
Probability is low, as you say they ALL read 0V. That also mostly discounts de-lamination / separation, when heat / currents etc force the
anodes / cathodes apart. Usually though, there is some leakage still. You could try to remove a cap and check again, even apply some pressure.
As far as parallel cells conditioning each other - this is quite true. In all my packs, I have up to 7+ paralleled in each block.
www.pbase.com/digsys/image/164509549 Some notes -
equalization is greatest during large charge / discharge cycles AND at the ends of their capacity. ie ~5% at the top ~3.8V-4.2V and ~10%
at the bottom ~3.2V-0.5V. When the cells are in their middle-state, capacity range of app ~80%, the voltage only varies from ~3.65-3.75V
Add tolerance variations between cells and there is only little equalization occurring when in trickle / low power modes.
One good piece of news is - in the 1000s of cells we've gone through, most failures are open-circuit / high impedance (as what you MAY be seeing).
In a parallel block, the O/C cell just doesn't exist - in a series block, the entire string goes O/C, so failures rarely end in fires and gassing.
Usually, they look like this -
www.pbase.com/digsys/image/164509551 (note: we do use all types of cell types / packaging)
Fires / serious failures are usually under very high currents (exceeding C ratings etc) and/or high temperatures OR physical damage.
You have nothing to lose by removing the cap(s) and investigating further.