New Tesla's have a lithium battery. The reason for the 12V is that the low voltage electrical system can periodically need to deliver and control ~100A @ 12V. To do this with DC to DC conversion from the ~400V main pack is complex and expensive. The legacy auto industry supply chain won't switch from 12V further complicating the economics of a better design.
If your Tesla senses a fault in the low voltage system it will cut the connection to the high voltage pack and send you a message saying "pull over your car may not restart" depending on the fault, this message will stay up for hours or even days. At this point your 12V batter is no longer being recharged. Once the battery gets really low the warning messages get more intense and the car will literally not move. At this point the doors still work, usually for hours. There is a ton of warning before your doors won't open.
This is for the lead acid case of older cars. Newer cars have a 12V lithium ion battery with higher capacity that may behave differently.
Next gen Tesla's (starting with the cybertruck) use 48V low voltage architecture that is 4x lower current. Tesla now has the scale to develop the 48V automotive supply chain internally in spite of the resistance from incumbent OEMs.
