How does a dead battery look in a circuit?
By the time a "car battery" gets down to 12 volts, it is considered dead (mostly dead, Princess Bride). Although I think I would agree with you that my first instinct was to think of 0 volts. When I thought about it scientifically, and looked it up :  


  Other Helpful Voltages
  
  Battery voltage can be higher than 12.6 volts immediately after charging.
  Open Circuit Voltage of 12V battery after car is off for one hour | Relative charge
  12.4V: 75%
  12.2V: 50%
  12.1V: 25%
  Less than 12 volts:    Dead  


I should give credit to : http://www.w8ji.com/battery_and_charging_system.htm  

View it this way: The internal resistance of the battery (when discharged) becomes high.  You could model the "dead" battery as 12 volts with a high resistance in series with the battery.